What is the total number of ways of choosing | vedclass

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

Vedclass · Accepted Answer

$270725$ and $2860$

Vedclass · Answer

(A) The total number of ways to choose $4$ cards from $52$ cards is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Total ways $= ^{52}C_{4} = \frac{52 	imes 51 	imes 50 	imes 49}{4 	imes 3 	imes 2 	imes 1} = 270725$.There are $4$ suits in a deck,each containing $13$ cards. To choose $4$ cards of the same suit,we must choose one suit out of $4$ and then choose $4$ cards from the $13$ available in that suit.Ways to choose $4$ cards of the same suit $= 4 	imes ^{13}C_{4} = 4 	imes \frac{13 	imes 12 	imes 11 	imes 10}{4 	imes 3 	imes 2 	imes 1} = 4 	imes 715 = 2860$.

What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the four cards of the same suit?

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