Practice variation 2 of 3
Combinatorics — Chain for n=2
Your question
(i) Use the identity to show that .
(ii) A club has members, with women and men. A group consisting of an even number of members is chosen, with equally many men and women. Show that the number of ways to do this is .
(iii) From the group chosen in part (ii), one of the men and one of the women are selected as leaders. Show that the number of ways to choose the even group and then the leaders is .
(iv) The process is now reversed: leaders are chosen first, then the rest of the balanced group. Using part (ii), find a simple expression for the sum in part (iii).
This practice question was inspired by Question 14(a) in the 2020 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?