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 $52$ is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Total ways $= ^{52}C_

Vedclass · Accepted Answer

$270725$ and $29900$

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 $= ^{52}C_{4} = \frac{52 	imes 51 	imes 50 	imes 49}{4 	imes 3 	imes 2 	imes 1} = 270725$.For the cards to be of the same colour,they must be either all red or all black.There are $26$ red cards and $26$ black cards.Ways to choose $4$ red cards $= ^{26}C_{4} = \frac{26 	imes 25 	imes 24 	imes 23}{4 	imes 3 	imes 2 	imes 1} = 14950$.Ways to choose $4$ black cards $= ^{26}C_{4} = 14950$.Total ways for same colour $= 14950 + 14950 = 29900$.

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 $4$ cards of the same colour?

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