Find the number of 5-card combinations out of a deck of 52 cards if a least one of the five cards has to be king.

Since there are 52 cards in a deck out of which 4 are king and others are non-kings.


So, the no. of ways are as follows:


1. 1 king and 4 non-king


2. 2 king and 3 non-king


3. 3 king and 2 non-king


4. 4 king and 1 non-king


So , total no. of ways are


= 4C1 48C4 + 4C2 48C3 + 4C3 48C2 + 4C4 48C1


Applying nCr =


= 778320+103776+4512+48


= 886656 ways.


1