How many ways are there to from a committee of 2 from 2m Ima

How many ways are there to from a committee of 2 from 2m Imagine you are in charge of forming the above committee from a pool of 2m applicant. Just for your pleasure you visually half of them in blue and the other half in red. How many way are there to from a committee of 2 such that both are How many ways are there to form a committee of 2 such that one is red and the other is blue. Use preceding answers to show that Give combinational argument to show that

Solution

a) Number of ways to form a committe = 2nC2 = 2n(2n-1)/2 = (2n^2 - n) ways

b) i)Since there are only n red applicants, hence number of ways will be nC2 = n(n-1)/2 = (n^2-n)/2 ways

ii) Selecting one from blue in nC1 ways

Selecting one from red in nC1 ways

Number of ways = nC1 * nC1 = n^2 ways

c)

2nC2 = 2n(2n-1)/2 = 2n^2 - n ways

2(nC2) = n(n-1) = n^2 - n ways

Hence we get 2nC2 = 2(nC2) + n^2