What is the number of ways of choosing 4 card | vedclass

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(B) The number of ways to choose $4$ cards from $52$ cards is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.For choosing $4$ card

Vedclass · Accepted Answer

$495$

Vedclass · Answer

(B) The number of ways to choose $4$ cards from $52$ cards is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.For choosing $4$ cards from $52$,we have $^{52}C_{4} = \frac{52 	imes 51 	imes 50 	imes 49}{4 	imes 3 	imes 2 	imes 1} = 270725$.There are $12$ face cards in a deck (Jack,Queen,King of each of the $4$ suits).The number of ways to select $4$ face cards out of $12$ is $^{12}C_{4} = \frac{12 	imes 11 	imes 10 	imes 9}{4 	imes 3 	imes 2 	imes 1} = 495$.

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are all $4$ cards face cards?

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