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?

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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