n white and n black balls in a bag

Question

A bag contains n white and n black balls. Pairs of balls are drawn at random without replacement successively , until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is 14,400 .Then find the value of n.  ANSWER-4

Answer 1

My combinatorial experience is rusty, but here is the way I'm tackling this question.

 

Total # of balls is 2n, but the number selected at each draw is 2 - 1B, 1W. So, there are n pairs, and the 'number selected' is 1.

 

Since _n C _r =14,400, then _14,400 C ₁ = 14,400, and n = 14,400. Total # balls is 28,800, but with the restriction that each pair has 1B and 1W - I won't use 'number selected' as 2.

 

Feeling a bit diffident and thinking it's too easy, please enlighten me.

 

Anita A.