Six cards are drawn simultaneously from a pac | vedclass

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(C) Total number of cards in a pack is $52$.There are $26$ red cards and $26$ black cards in a pack.We need to draw $6$ cards simultaneously,which can

Vedclass · Accepted Answer

$\frac{^{26}C_3 	imes ^{26}C_3}{^{52}C_6}$

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(C) Total number of cards in a pack is $52$.There are $26$ red cards and $26$ black cards in a pack.We need to draw $6$ cards simultaneously,which can be done in $^{52}C_6$ ways.The number of ways to select $3$ red cards from $26$ red cards is $^{26}C_3$.The number of ways to select $3$ black cards from $26$ black cards is $^{26}C_3$.Therefore,the number of favorable outcomes is $^{26}C_3 	imes ^{26}C_3$.The probability is given by the ratio of favorable outcomes to total outcomes: $P = \frac{^{26}C_3 	imes ^{26}C_3}{^{52}C_6}$.

Six cards are drawn simultaneously from a pack of playing cards. What is the probability that $3$ will be red and $3$ will be black?

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