1.) On the 28 projects being judged, the top 5 projects will recieve awards. In how many different ways the award can be given?
a. 120
b. 98,280
c. 11,793,600
d. 2.59 X 10^22
explain how
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2006-10-26 15:22:21 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
If the awards are all different, then it is
28*27*26*25*24 = 11,793,600
If the top 5 projects all receive the same award, then it is
11973600/(5!) = 11973600/120 = 98,280
2006-10-26 15:25:40 · answer #1 · answered by MsMath 7 · 0⤊ 2⤋
The answer is 28*27*26*25*24 = 11,793,600, which is answer (c).
28 of the projects can get first place
After that, 27 projects can get second place
After that, 26 projects can get third place
After that, 25 proejcts can get fourth place
After that, 24 projects can get fifth place
Thus, there are 28*27*26*25*24 ways that that can happen.
HOWEVER, if you feel that the problem is really asking how many different TOP 5 COMBINATIONS are there, then you need to consider that of those 28*27*26*25*24 = 11,793,600 ways that the top five places can be given out, there are 5*4*3*2*1 ways that the same five top projects can be put into those places. That is,
The first place could be rearranged into any of the 5 places
After that the second place could be put in any of the remaining 4
After that the third place could be put in any of the remaining 3
After that the fourth place could be put in any of the remaining 2
After that the fifth place would have to be put in the last remaining spot
Thus, for any top 5 projects (a,b,c,d,e), there are 5*4*3*2*1 ways to arrange them in the top 5 places. In other words, there are 5*4*3*2*1 "permutations" of (a,b,c,d,e).
Thus, there are 28*27*26*25*24/(5*4*3*2*1) = 98280 TOP 5 COMBINATIONS. However, there are 28*27*26*25*24=11,793,600 TOP 5 PERMUTATIONS.
Combinations are given with (n choose k) = n!/[ (n-k)! k! ].
Permutations are given with n!/[ (n-k)! ].
In both cases, n = 28 and k = 5.
2006-10-26 22:30:19 · answer #2 · answered by Ted 4 · 1⤊ 0⤋
C, 11,793,600.
First, there are 28 projects to be judged. After First Place is chosen, there will be 27 left. This can happen in 28*27 ways. After that, there are 26 different projects eligible to win, and that continues til 23. 23*24*25*26*27*28 = 11,793,600.
2006-10-26 22:26:17 · answer #3 · answered by Anonymous · 0⤊ 1⤋
28 of the projects can get first place
After that, 27 projects can get second place
After that, 26 projects can get third place
After that, 25 projects can get fourth place
After that, 24 projects can get fifth place
There are 28*27*26*25*24 ways that can happen
There are 11, 793,600 ways
2006-10-28 00:39:11 · answer #4 · answered by Akilesh - Internet Undertaker 7 · 0⤊ 0⤋
1st prize, there are 28 choices. There are 27 left to pick from for the 2nd prize etc so:
28*27*26*25*24=11,793,600
answer is c. 11,793,600
2006-10-27 00:43:56 · answer #5 · answered by yupchagee 7 · 0⤊ 0⤋
28 nPr 5= 28*27*26*25*24=11,793,600
28!/(28-5)!
C
2006-10-26 22:27:34 · answer #6 · answered by Ivan 2 · 0⤊ 1⤋
5. 1st place 2nd place 3rd place 4th place 5th place i before e except after c.
2006-10-26 22:29:59 · answer #7 · answered by gone 7 · 0⤊ 1⤋
Hi. 5! ..... That's 5 factorial... that's 5x4x3x2x1=??
2006-10-26 22:25:21 · answer #8 · answered by Cirric 7 · 0⤊ 4⤋