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