Question

All the face cards are removed from a well-shuffled pack of $52$ cards. Out of the remaining cards, $4$ cards are drawn at random. The probability that they belong to different suits is

• A. $\frac{{}^{13}{C}_4}{{}^{40}{C}_4}$
• B. $\frac{{10}^4}{{}^{52}{C}_4}$
• C. $\frac{{13}^4}{{}^{40}{C}_4}$
• D. $\frac{{10}^4}{{}^{40}{C}_4}$

Answer 1

The correct option is D $\frac{{10}^4}{{}^{40}{C}_4}$

After the removal of face cards, total number of remaining cards is $40.$
Total number of ways of selecting $4$ cards from $40$ cards is ${}^{40}{C}_4.$
Favourable ways of $4$ cards belonging to different suits $={}^{10}{C}_1\times {}^{10}{C}_1\times {}^{10}{C}_1\times {}^{10}{C}_1={10}^4$
$\therefore$ Required probability $=\frac{{10}^4}{{}^{40}{C}_4}$