students in maths test can score 0,1,2 or3 marks on each of six questions. There is only one way of scoring 18 and 6 ways of scoring 17. the number of ways a student can score sixteen is?
A:6
B:12
C:15
D:21
E:42
please show how you worked this out.
2006-07-10 15:02:56 · 7 answers · asked by hello 2 in Science & Mathematics ➔ Mathematics
Six ways with 5 questions getting 3 and 1 question getting 1 (lose 2 points on a single question):
333331
333313
333133
331333
313333
133333
Fifteen ways with 4 scores of 3 and 2 scores of 2 (lose 1 point on two different questions):
333322
333223
333232
332332
332323
332233
323332
323323
323233
322333
233332
233323
233233
232333
223333
This is also 6C1 + 6C2
6C1 = 6!/(5!*1!) = 6
6C2 = 6!/(4!*2!) = 15
Total of 21 ways:
D. 21
2006-07-10 15:08:11 · answer #1 · answered by Puzzling 7 · 4⤊ 0⤋
There is only 1 way of scoring 18,
3+3+3+3+3+3 = 18
There are 6 ways of scoring 17,
1. 3+3+3+3+3+2 = 17
2. 3+3+3+3+2+3 = 17
3. 3+3+3+2+3+3 = 17
4. 3+3+2+3+3+3 = 17
5. 3+2+3+3+3+3 = 17
6. 2+3+3+3+3+3 = 17
Numbers of ways to score 16 is,
1. 3+3+3+3+2+2 = 16
2. 3+3+3+2+3+2 = 16
3. 3+3+3+2+2+3 = 16
4. 3+3+2+3+3+2 = 16
5. 3+3+2+3+2+3 = 16
6. 3+3+2+2+3+3 = 16
7. 3+2+3+3+3+2 = 16
8. 3+2+3+3+2+3 = 16
9. 3+2+3+2+3+3 = 16
10. 3+2+2+3+3+3 = 16
11. 2+3+3+3+3+2 = 16
12. 2+3+3+3+2+3 = 16
13. 2+3+3+2+3+3 = 16
14. 2+3+2+3+3+3 = 16
15. 2+2+3+3+3+3 = 16
16. 3+3+3+3+3+1 = 16
17. 3+3+3+3+1+3 = 16
18. 3+3+3+1+3+3 = 16
19. 3+3+1+3+3+3 = 16
20. 3+1+3+3+3+3 = 16
21. 1+3+3+3+3+3 = 16
Therefore, the answer is
D: 21
2006-07-10 22:33:36 · answer #2 · answered by ideaquest 7 · 0⤊ 0⤋
why is only one way of scoring 18?? because 18 is the maximum so the only way is getting three points on every answer. To score 17 you can loose only one point on every of the question and since there are 6 question there are six ways of scoring 17. now with sixteen is more complicated because either you loose two points in the same question or you loose on point on two of them. Supposing that you loose two points in one question you have six ways of scoring sixteen now the other combinations are
loosing one point on two that can be:
1-2 1-3 1-4 1-5 1-6
2-3 2-4 2-5 2-6
3-4 3-5 3-6
4-5 4-6
5-6
*notice that there are no 3-3 or 4-4 because you count them already supossing that you loose two points on any answer.
so now you add 6+15=21
21 is the right answer (((((c)))))
2006-07-10 22:16:26 · answer #3 · answered by el cuyo 2 · 0⤊ 0⤋
The answer would be 21
2006-07-10 22:42:31 · answer #4 · answered by Shorti 2 · 0⤊ 0⤋
It's easy if You put the 7% of your brain that you use to use. Try it and see the majical things that will happen.
2006-07-10 22:07:33 · answer #5 · answered by eezypeezy92 3 · 0⤊ 0⤋
21 ofcourse...
2006-07-10 22:08:55 · answer #6 · answered by arpitjain11 1 · 0⤊ 0⤋
do ur own homework
2006-07-10 22:07:12 · answer #7 · answered by D-Wade is the MVP 1 · 0⤊ 0⤋