Solution: n C9 = n C8 Or n!/ 9!( n-9)! = n!/ 8!( n-8)! Or n!/ 9 * 8!( n-9)! = n!/ 8!( n-8)*( n-9)! Or n = 17
n C16 = 17 C16 = 17
Numerical: What is number of ways to select 4 cards from a pack of 52 playing cards? In how many:
o four cards are of the same suit, o four cards belong to four different suits, o are face cards, o two are red cards and two are black cards, o cards are of the same colour?
Solution: Out of total 52 cards, there are 12 Face cards( J, K, Q)
1) Ways to draw 4 cards of same suit = Ways to draw 4 cards of( diamond + Heart + Club + Space) suit
= 13 C4 + 13 C4 + 13 C4 + 13 C4 = 2860