From http://www.sgforums.com/forums/2297/topics/409229

a) There is a committee of 5 boys and 3 girls. At a meeting, 2 boys are absent. Find the number of ways they can sit at a round table with 8 seats.

b) A deck of 10 cards is numbered from 0 to 9. Find the number of ways 5 cards can be chosen such that the sum of the chosen cards is larger than those not chosen.

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**Answer:**a) Factorial 8 different seats, but 2 are "repeated" as empty seats

Hence, the answer is

(8 - 1)! / 2! =

**2520**

b) There are

^{10}C

_{5}ways of choosing 5 cards without restriction

The 5 cards chosen is either bigger than or lesser than the cards not chosen.

The probability that the chosen cards are greater than the "unchosen" cards is equal to the probability that the chosen cards are lesser than the "unchosen" cards

Hence we can just take

^{10}C

_{5}divide by 2 =

**126**