From a pack of 52 cards, 3 cards are drawn at random. Then, the probability that one is ace, one is queen…
From a pack of 52 cards, 3 cards are drawn at random. Then, the probability that one is ace, one is queen and one is jack is
$\frac{19}{5525}$
$\frac{21}{5525}$
$\frac{17}{5525}$
$\frac{16}{5525}$
Solution
Favourable outcomes
$\Rightarrow$ One ace and one queen and 1 jack
There are 4 cards of each
Selecting 1 out of 4 can be done in
${ }^4 C_1 \times{ }^4 C_1 \times{ }^4 C_1=4 \times 4 \times 4$ ways
There are total 52 cards
Total outcomes are selecting 3 out of 52
i.e. ${ }^{52} \mathrm{C}_3=\frac{52 \times 51 \times 50}{3 \times 2}=22100$
Required probability $=\frac{4 \times 4 \times 4}{22100}$
$=\frac{16}{5525}$