Can you help me settle the great math debate?

Question

From my daughters home work......

How many license plates can you make with the letters M N P and the numbers 1 2 3, if each plate starts with 3 letters and ends with 3 numbers?

My husband has one answer and I have another can you tell me which is right?

Answer 1

3*2*1*3*2*1 = 36

Explanation: the first point, you can pick M, N or P. If you choose M, then only N or P is available for the second slot. If you pick N, then only P is available. So, 3 choices * 2 choices * 1 choice. Repeat for the numerals.

=========
UNLESS you can choose M N or P more than once, and same for 1, 2 or 3

Then it's 3*3*3*3*3*3 = 729

Answer 2

729 ...

1. PPP111
2. NPP111
3. MPP111
4. PNP111
5. NNP111
6. MNP111
7. PMP111
8. NMP111
9. MMP111
10. PPN111
11. NPN111
12. MPN111
13. PNN111
14. NNN111
15. MNN111
16. PMN111
17. NMN111
18. MMN111
19. PPM111
20. NPM111
21. MPM111
22. PNM111
23. NNM111
24. MNM111
25. PMM111
26. NMM111
27. MMM111
28. PPP211
29. NPP211
30. MPP211
31. PNP211
32. NNP211
33. MNP211
34. PMP211
35. NMP211
36. MMP211
37. PPN211
38. NPN211
39. MPN211
40. PNN211
41. NNN211
42. MNN211
43. PMN211
44. NMN211
45. MMN211
46. PPM211
47. NPM211
48. MPM211
49. PNM211
50. NNM211
51. MNM211
52. PMM211
53. NMM211
54. MMM211
55. PPP311
56. NPP311
57. MPP311
58. PNP311
59. NNP311
60. MNP311
61. PMP311
62. NMP311
63. MMP311
64. PPN311
65. NPN311
66. MPN311
67. PNN311
68. NNN311
69. MNN311
70. PMN311
71. NMN311
72. MMN311
73. PPM311
74. NPM311
75. MPM311
76. PNM311
77. NNM311
78. MNM311
79. PMM311
80. NMM311
81. MMM311
82. PPP121
83. NPP121
84. MPP121
85. PNP121
86. NNP121
87. MNP121
88. PMP121
89. NMP121
90. MMP121
91. PPN121
92. NPN121
93. MPN121
94. PNN121
95. NNN121
96. MNN121
97. PMN121
98. NMN121
99. MMN121
100. PPM121
101. NPM121
102. MPM121
103. PNM121
104. NNM121
105. MNM121
106. PMM121
107. NMM121
108. MMM121
109. PPP221
110. NPP221
111. MPP221
112. PNP221
113. NNP221
114. MNP221
115. PMP221
116. NMP221
117. MMP221
118. PPN221
119. NPN221
120. MPN221
121. PNN221
122. NNN221
123. MNN221
124. PMN221
125. NMN221
126. MMN221
127. PPM221
128. NPM221
129. MPM221
130. PNM221
131. NNM221
132. MNM221
133. PMM221
134. NMM221
135. MMM221
136. PPP321
137. NPP321
138. MPP321
139. PNP321
140. NNP321
141. MNP321
142. PMP321
143. NMP321
144. MMP321
145. PPN321
146. NPN321
147. MPN321
148. PNN321
149. NNN321
150. MNN321
151. PMN321
152. NMN321
153. MMN321
154. PPM321
155. NPM321
156. MPM321
157. PNM321
158. NNM321
159. MNM321
160. PMM321
161. NMM321
162. MMM321
163. PPP131
164. NPP131
165. MPP131
166. PNP131
167. NNP131
168. MNP131
169. PMP131
170. NMP131
171. MMP131
172. PPN131
173. NPN131
174. MPN131
175. PNN131
176. NNN131
177. MNN131
178. PMN131
179. NMN131
180. MMN131
181. PPM131
182. NPM131
183. MPM131
184. PNM131
185. NNM131
186. MNM131
187. PMM131
188. NMM131
189. MMM131
190. PPP231
191. NPP231
192. MPP231
193. PNP231
194. NNP231
195. MNP231
196. PMP231
197. NMP231
198. MMP231
199. PPN231
200. NPN231
201. MPN231
202. PNN231
203. NNN231
204. MNN231
205. PMN231
206. NMN231
207. MMN231
208. PPM231
209. NPM231
210. MPM231
211. PNM231
212. NNM231
213. MNM231
214. PMM231
215. NMM231
216. MMM231
217. PPP331
218. NPP331
219. MPP331
220. PNP331
221. NNP331
222. MNP331
223. PMP331
224. NMP331
225. MMP331
226. PPN331
227. NPN331
228. MPN331
229. PNN331
230. NNN331
231. MNN331
232. PMN331
233. NMN331
234. MMN331
235. PPM331
236. NPM331
237. MPM331
238. PNM331
239. NNM331
240. MNM331
241. PMM331
242. NMM331
243. MMM331
244. PPP112
245. NPP112
246. MPP112
247. PNP112
248. NNP112
249. MNP112
250. PMP112
251. NMP112
252. MMP112
253. PPN112
254. NPN112
255. MPN112
256. PNN112
257. NNN112
258. MNN112
259. PMN112
260. NMN112
261. MMN112
262. PPM112
263. NPM112
264. MPM112
265. PNM112
266. NNM112
267. MNM112
268. PMM112
269. NMM112
270. MMM112
271. PPP212
272. NPP212
273. MPP212
274. PNP212
275. NNP212
276. MNP212
277. PMP212
278. NMP212
279. MMP212
280. PPN212
281. NPN212
282. MPN212
283. PNN212
284. NNN212
285. MNN212
286. PMN212
287. NMN212
288. MMN212
289. PPM212
290. NPM212
291. MPM212
292. PNM212
293. NNM212
294. MNM212
295. PMM212
296. NMM212
297. MMM212
298. PPP312
299. NPP312
300. MPP312
301. PNP312
302. NNP312
303. MNP312
304. PMP312
305. NMP312
306. MMP312
307. PPN312
308. NPN312
309. MPN312
310. PNN312
311. NNN312
312. MNN312
313. PMN312
314. NMN312
315. MMN312
316. PPM312
317. NPM312
318. MPM312
319. PNM312
320. NNM312
321. MNM312
322. PMM312
323. NMM312
324. MMM312
325. PPP122
326. NPP122
327. MPP122
328. PNP122
329. NNP122
330. MNP122
331. PMP122
332. NMP122
333. MMP122
334. PPN122
335. NPN122
336. MPN122
337. PNN122
338. NNN122
339. MNN122
340. PMN122
341. NMN122
342. MMN122
343. PPM122
344. NPM122
345. MPM122
346. PNM122
347. NNM122
348. MNM122
349. PMM122
350. NMM122
351. MMM122
352. PPP222
353. NPP222
354. MPP222
355. PNP222
356. NNP222
357. MNP222
358. PMP222
359. NMP222
360. MMP222
361. PPN222
362. NPN222
363. MPN222
364. PNN222
365. NNN222
366. MNN222
367. PMN222
368. NMN222
369. MMN222
370. PPM222
371. NPM222
372. MPM222
373. PNM222
374. NNM222
375. MNM222
376. PMM222
377. NMM222
378. MMM222
379. PPP322
380. NPP322
381. MPP322
382. PNP322
383. NNP322
384. MNP322
385. PMP322
386. NMP322
387. MMP322
388. PPN322
389. NPN322
390. MPN322
391. PNN322
392. NNN322
393. MNN322
394. PMN322
395. NMN322
396. MMN322
397. PPM322
398. NPM322
399. MPM322
400. PNM322
401. NNM322
402. MNM322
403. PMM322
404. NMM322
405. MMM322
406. PPP132
407. NPP132
408. MPP132
409. PNP132
410. NNP132
411. MNP132
412. PMP132
413. NMP132
414. MMP132
415. PPN132
416. NPN132
417. MPN132
418. PNN132
419. NNN132
420. MNN132
421. PMN132
422. NMN132
423. MMN132
424. PPM132
425. NPM132
426. MPM132
427. PNM132
428. NNM132
429. MNM132
430. PMM132
431. NMM132
432. MMM132
433. PPP232
434. NPP232
435. MPP232
436. PNP232
437. NNP232
438. MNP232
439. PMP232
440. NMP232
441. MMP232
442. PPN232
443. NPN232
444. MPN232
445. PNN232
446. NNN232
447. MNN232
448. PMN232
449. NMN232
450. MMN232
451. PPM232
452. NPM232
453. MPM232
454. PNM232
455. NNM232
456. MNM232
457. PMM232
458. NMM232
459. MMM232
460. PPP332
461. NPP332
462. MPP332
463. PNP332
464. NNP332
465. MNP332
466. PMP332
467. NMP332
468. MMP332
469. PPN332
470. NPN332
471. MPN332
472. PNN332
473. NNN332
474. MNN332
475. PMN332
476. NMN332
477. MMN332
478. PPM332
479. NPM332
480. MPM332
481. PNM332
482. NNM332
483. MNM332
484. PMM332
485. NMM332
486. MMM332
487. PPP113
488. NPP113
489. MPP113
490. PNP113
491. NNP113
492. MNP113
493. PMP113
494. NMP113
495. MMP113
496. PPN113
497. NPN113
498. MPN113
499. PNN113
500. NNN113
501. MNN113
502. PMN113
503. NMN113
504. MMN113
505. PPM113
506. NPM113
507. MPM113
508. PNM113
509. NNM113
510. MNM113
511. PMM113
512. NMM113
513. MMM113
514. PPP213
515. NPP213
516. MPP213
517. PNP213
518. NNP213
519. MNP213
520. PMP213
521. NMP213
522. MMP213
523. PPN213
524. NPN213
525. MPN213
526. PNN213
527. NNN213
528. MNN213
529. PMN213
530. NMN213
531. MMN213
532. PPM213
533. NPM213
534. MPM213
535. PNM213
536. NNM213
537. MNM213
538. PMM213
539. NMM213
540. MMM213
541. PPP313
542. NPP313
543. MPP313
544. PNP313
545. NNP313
546. MNP313
547. PMP313
548. NMP313
549. MMP313
550. PPN313
551. NPN313
552. MPN313
553. PNN313
554. NNN313
555. MNN313
556. PMN313
557. NMN313
558. MMN313
559. PPM313
560. NPM313
561. MPM313
562. PNM313
563. NNM313
564. MNM313
565. PMM313
566. NMM313
567. MMM313
568. PPP123
569. NPP123
570. MPP123
571. PNP123
572. NNP123
573. MNP123
574. PMP123
575. NMP123
576. MMP123
577. PPN123
578. NPN123
579. MPN123
580. PNN123
581. NNN123
582. MNN123
583. PMN123
584. NMN123
585. MMN123
586. PPM123
587. NPM123
588. MPM123
589. PNM123
590. NNM123
591. MNM123
592. PMM123
593. NMM123
594. MMM123
595. PPP223
596. NPP223
597. MPP223
598. PNP223
599. NNP223
600. MNP223
601. PMP223
602. NMP223
603. MMP223
604. PPN223
605. NPN223
606. MPN223
607. PNN223
608. NNN223
609. MNN223
610. PMN223
611. NMN223
612. MMN223
613. PPM223
614. NPM223
615. MPM223
616. PNM223
617. NNM223
618. MNM223
619. PMM223
620. NMM223
621. MMM223
622. PPP323
623. NPP323
624. MPP323
625. PNP323
626. NNP323
627. MNP323
628. PMP323
629. NMP323
630. MMP323
631. PPN323
632. NPN323
633. MPN323
634. PNN323
635. NNN323
636. MNN323
637. PMN323
638. NMN323
639. MMN323
640. PPM323
641. NPM323
642. MPM323
643. PNM323
644. NNM323
645. MNM323
646. PMM323
647. NMM323
648. MMM323
649. PPP133
650. NPP133
651. MPP133
652. PNP133
653. NNP133
654. MNP133
655. PMP133
656. NMP133
657. MMP133
658. PPN133
659. NPN133
660. MPN133
661. PNN133
662. NNN133
663. MNN133
664. PMN133
665. NMN133
666. MMN133
667. PPM133
668. NPM133
669. MPM133
670. PNM133
671. NNM133
672. MNM133
673. PMM133
674. NMM133
675. MMM133
676. PPP233
677. NPP233
678. MPP233
679. PNP233
680. NNP233
681. MNP233
682. PMP233
683. NMP233
684. MMP233
685. PPN233
686. NPN233
687. MPN233
688. PNN233
689. NNN233
690. MNN233
691. PMN233
692. NMN233
693. MMN233
694. PPM233
695. NPM233
696. MPM233
697. PNM233
698. NNM233
699. MNM233
700. PMM233
701. NMM233
702. MMM233
703. PPP333
704. NPP333
705. MPP333
706. PNP333
707. NNP333
708. MNP333
709. PMP333
710. NMP333
711. MMP333
712. PPN333
713. NPN333
714. MPN333
715. PNN333
716. NNN333
717. MNN333
718. PMN333
719. NMN333
720. MMN333
721. PPM333
722. NPM333
723. MPM333
724. PNM333
725. NNM333
726. MNM333
727. PMM333
728. NMM333
729. MMM333

Answer 3

The letters all have to be on the left side of the plate, and exactly 3 have to be chosen. Assuming we can have repeating letters (e.g, "MPP", "NNN", etc. are allowed -- and if we can't allow this, then see the last paragraph), there are 3*3*3 = 27 different ways you can take a combination of the letters M, N, or P and make a set of three letters in a row.

Similarly, the numbers all have to be on the right side of the place, and exactly 3 of the digits have to be chosen. Assuming we can have repeating digits, and we only have three different digits to choose from, then again there would be 3*3*3 = 27 different ways you can print a trio of numbers on the license plate.

Since the left side can be one of 27 combinations, and the right side can be one of 27 combinations, then the total number of possible license plates are 27*27 = 729.

Again, this assumes you can have any of these letters or numbers repeating. If you CAN'T, then it's a different story. If you're only given one M, one N and one P to work with, there are only 3*2*1 = 6 different ways you can arrange these three letters to get a new sequence: MNP, MPN, NMP, NPM, PMN and PNM. Likewise with the numbers, there are only 6 different ways you can rearrange "1" "2" and "3". So with these limitations, you can only have 6*6 = 36 different license plates.

Answer 4

Allowing for repetition of letter/numbers:
On the plate, for the first character, you have 3 choices: M ,N, P. For each of those choices, you have 3 choices for the second character: M, N, P. That gives you 9 choices so far, or 3^2. For the third character, you again have 3 choices for each of your previous 9 possibilities, giving 27, or 3^3. Beginning to see the pattern? There are 6 characters on the plate, so 3^6 = 729 is the number of license plates you can make.

If no repetition is allowed:
On the plate, for the first character, you have 3 choices: M, N, P. For the second character, you already used one letter, so there are 2 choices left, giving 6 combinations. The last character is the last letter, so there is only one choice. You have 6 possible combinations of letter. The same is true of the numbers. So you have 6*6 = 36 possible license plates.

Answer 5

Okay a combination of three letters. There are 6 possible

M N P
M P N
N M P
N P M
P N M
P M N (You also have six possibilities for 1 2 3 )

All six possible number combinations can fit behind each of the letter combinations so the answer is 6 x 6 or 36

OF course I am assuming those exact letters so PPP 111 is not a possibility.

Answer 6

36. i forget what it is called but it goes like this.
1) Your first letter can be 1 of 3 options
2) Your 2nd letter can be 1 of 2 options
3) Leaves with 1 opiton for your 3rd letter

3*2*1=6

4)repeat this with th numbers
5) multiply your first set by the second set.
6*6=36

This is assuming that none of the letters or numbers can repeat themselves. Otherwise youd would get 729 (3*3*3=27) [27*27=729]

Answer 7

729