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.
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.

Answer : 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 of ways are

= 4C1 X48C4 + 4C2X48C3 + 4C3 X48C2 + 4C4X48C1

= 778320+103776+4512+48

= 886656 ways.