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Ben and Ann are among 7 contestants from which 4 [#permalink]
28 Jan 2004, 15:58

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A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

19. Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann?
(A) 5
(B) 6
(C) 7
(D) 14
(E) 21

Padma, I did the traditional way, lets say 1,2,3,4,5,Ben and Ann are 7 contestants. First Ben and Ann are ruled out, we r left with 1,2,3,4,5 and so the possible selections are 1234, 1235, 1245,1345 and 2345.

Well this is tricky. It lets you comeout with 7C4- 2 * 5C2 = 15
But what we need is 4 contestants out of 5 since we are to exclude A&B
The answer is simply 5C4 = 5

I wish stoolfi has some innovative method to explain the discrepency here.

Well I have the innovative way. I hate to depart from classical way to solve this.

Let us say we have chosen A & B now now we choose 2 out of remaining 5
we get a pair and let us call it C
so we have A,B,C we can arrange these in 3 ways
(A,B,C), (C,A,B), (B,C,A)
so we have 3 * 5C2 combinations in which A and B are present = 30
Total combinations = 7C4 = 35

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...