(C) Total number of ways to draw $2$ cards from $52$ is $^{52}C_2 = \frac{52 \times 51}{2 \times 1} = 1326$.There are $12$ face cards ($J, Q, K$ of ea

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(C) Total number of ways to draw $2$ cards from $52$ is $^{52}C_2 = \frac{52 \times 51}{2 \times 1} = 1326$.There are $12$ face cards ($J, Q, K$ of each suit) and $4$ ace cards in a deck.The number of ways to choose $1$ face card from $12$ is $^{12}C_1 = 12$.The number of ways to choose $1$ ace card from $4$ is $^4C_1 = 4$.The number of favorable outcomes is $12 \times 4 = 48$.The probability is $\frac{48}{1326} = \frac{24}{663} = \frac{8}{221}$.

Class 11 Mathematics Probability Advanced Use of permutations and combinations in probability

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Two cards are drawn at random from a standard pack of $52$ cards. The probability that the draw consists of exactly one face card and exactly one ace card is

MHT CET 2026 All MHT CET

A
$\frac{7}{221}$
B
$\frac{5}{221}$
C
$\frac{8}{221}$
D
$\frac{9}{221}$

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Advanced Use of permutations and combinations in probability

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