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

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

Vedclass · Accepted Answer

$270725$ and $105625$

Vedclass · Answer

(A) The total number of ways to choose $4$ cards from $52$ 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 $26$ red cards and $26$ black cards in a deck.To choose $2$ red cards from $26$ and $2$ black cards from $26$,the number of ways is $^{26}C_{2} 	imes ^{26}C_{2}$.$^{26}C_{2} = \frac{26 	imes 25}{2 	imes 1} = 325$.So,the required number of ways $= 325 	imes 325 = 105625$.

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are two red cards and two black cards?

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