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by thephoenix » Mon Feb 22, 2010 10:35 pm
Five cards are to be selected from 10 cards numbered 1 to 10. In how many ways can the cards be selected so that the average of the five numbers selected is greater than their median?

(A) 111
(B) 116
(C) 222
(D) 232
(E) 252
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by ajith » Wed Feb 24, 2010 12:34 am
thephoenix wrote:Five cards are to be selected from 10 cards numbered 1 to 10. In how many ways can the cards be selected so that the average of the five numbers selected is greater than their median?

(A) 111
(B) 116
(C) 222
(D) 232
(E) 252
I searched on the web and found out that one approach to solve this is

1. Find the no of ways in which one can select 5 cards from 10
2. Find the no of ways in which one can select 5 cards such that the mean of the numbers = median of the numbers
3. Find the no of ways in which mean not equal to median
4. By symmetry half of these should have mean> median and half will have mean <median

Which yields an answer of A

Anybody has any better approach?
Always borrow money from a pessimist, he doesn't expect to be paid back.
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