SOLUTION: How many ways can we select five door prizes from seven different ones and distribute them among five people?

Question 1200348: How many ways can we select five door prizes from seven different ones and distribute them among five people?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.

In 7*6*5*4*3 = 2520 different ways. ANSWER 1st person can get any one of the 7 prizes; 2nd person can get any one of the remaining 6 prizes; 3rd person can get any one of the remaining 5 prizes, and so on. The resulting number is the product of 5 consecutive positive integer numbers, starting from 7 in descending order.

Solved, with full explanations.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

In my opinion, the poor wording of the problem allows different interpretations; but they lead to the same answer.

Probably the intended interpretation is as shown in the response from the other tutor: 1 of the seven prizes is given to the first person, then 1 of the remaining 6 is given to the second person, and so on until 1 of the remaining 3 prizes is given to the fifth person. The answer is then 7*6*5*4*3 = 2520.

But another possible interpretation is that 5 of the 7 prizes are selected, AFTER WHICH they are given to 5 people. The number of ways of choosing 5 of the 7 prizes is C(7,5) = 21; then the number of ways to distribute them to the 5 people is 5*4*3*2*1 = 120. And so the answer using this interpretation is 21*120 = 2520.

Either way....

ANSWER: 2520

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