Q. 224.0( 5 Votes )

Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?

Answer :

Given that we need to draw 5 cards from a deck of 52 cards.


We need to find the no. of ways that at least one of the 5 cards has to be a king.


We know that there are 4 kings present in a deck.


Let us assume the no. of ways of drawing cards be N.


N = (Total no. of ways of drawing 5 cards out of 52 cards) – (No. of ways of drawing 5 cards without a king from remaining 48 cards)


N = (52C5) – (48C5)


We know that ,


And also n! = (n)(n – 1)......2.1





N = 2598960 – 1712304


N = 886656


The no. of ways of drawing 5 cards with at least 1 king is 886656.


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