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?
Question:

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?

Solution:

There are 4 kings in the deck of cards.

So, we are left with 48 cards out of 52.

$\therefore$ Required combination $={ }^{48} C_{1} \times{ }^{4} C_{4}+{ }^{48} C_{2} \times{ }^{4} C_{3}+{ }^{48} C_{3} \times{ }^{4} C_{2}+{ }^{48} C_{4} \times{ }^{4} C_{1}$

$=48+4512+103776+778320$

 

$=886656$

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