# Thread: Combinatorics Problems - great fun

1. ## Combinatorics Problems - great fun

A club consists of 25 married couples. Determine how many ways a committee of 7 people can be formed from these couples if:

a) there are no restrictions (1 mark)

b) there are exactly 5 men on the committee (2 marks)

c) at least one person must be a man (2 marks)

d) there must be at least 3 women and at least 2 men (4 marks)

$\displaystyle \sum\limits_{k = 3}^5 {{25 \choose k}{25 \choose {7-k}}}$