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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