(D) The total number of ways to select $3$ cards from $52$ is given by ${}^{52}C_3 = \frac{52 \times 51 \times 50}{3 \times 2 \times 1} = 22100$. Favo

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(D) The total number of ways to select $3$ cards from $52$ is given by ${}^{52}C_3 = \frac{52 \times 51 \times 50}{3 \times 2 \times 1} = 22100$. Favourable outcomes involve selecting $1$ ace from $4$,$1$ queen from $4$,and $1$ jack from $4$. This can be done in ${}^{4}C_1 \times {}^{4}C_1 \times {}^{4}C_1 = 4 \times 4 \times 4 = 64$ ways. The required probability is $\frac{64}{22100} = \frac{16}{5525}$.

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

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From a pack of $52$ cards,$3$ cards are drawn at random. Then,the probability that one is an ace,one is a queen,and one is a jack is

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A
$\frac{19}{5525}$
B
$\frac{21}{5525}$
C
$\frac{17}{5525}$
D
$\frac{16}{5525}$

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