Combinatorics, Question 2 (by T. Madas)

The Oakwood Jogging Club consists of 7 men and 6 women who go for a 5 mile run every Thursday. It is decided that a team of 8 runners would be picked at random out of the 13 runners, to represent the club at a larger meeting. Determine the proportion of teams of 8 , which have more women than men?

(the first person to publish a video on the problem will be able to choose the subject of our next meeting!)

Combinatorics question (by T. Madas)

A committee of 4 people is to be chosen at random from the members of a school council which consists of 5 pupils, 4 teachers and 3 administrators.

Determine the probability that the committee will contain:

a) no teachers.

b) … at least 2 pupils, no more than 1 teacher and no more than 1 administrator.