SOLUTION: Seven equally qualified students apply for a scholarship, but only five scholarships equal in value, can be given. How many ways can the five winners be selected?

Question 256421: Seven equally qualified students apply for a scholarship, but only five scholarships equal in value, can be given. How many ways can the five winners be selected?
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Seven equally qualified students apply for a scholarship, but only five scholarships equal in value, can be given. How many ways can the five winners be selected?
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The 1st selection is 1 of 7, then 1 of 6, then 1 of 5, etc
7*6*5*4*3 = 2520
But selecting A, B, C, D and E is the same as B, C, E, D and A. Person A has 5 chances to be selected. The 2nd has 4 chances to be selected, etc. 5*4*3*2*1 = 120.
The number of possible combinations is 2520/120 = 21
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To make it simpler, find the number of different ways 2 people are not selected:
The 1st is one of 7, the 2nd is one of 6 --> 7*6 = 42.
A and B is the same as B and A, so divide by 2
42/2 = 21.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Seven equally qualified students apply for a scholarship, but only five scholarships equal in value, can be given. How many ways can the five winners be selected?
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7C5 = 7C2 = (7*6)/(1*2) = 21
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Cheers,
Stan H.
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