Question

What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these four cards are of the same suit.

• A. $2860$
• B. $715$
• C. $270275$
• D. $1430$
• E. none of these

Answer 1

The correct option is A $2860$

The number of ways of choosing $4$ cards from a pack of $52$ playing cards

${=}^{52}{C}_4=\frac{52!}{4!48!}=\frac{52\times 51\times 50\times 49}{1\times 2\times 3\times 4}=270725$

The number of ways of choosing $4$ cards of same suit

${=}^{13}{C}_4=\frac{13!}{4!9!}=\frac{13\times 12\times 11\times 10}{1\times 2\times 3\times 4}=715$

Since there are $4$ suits, therefore, the number of ways of choosing $4$ cards of one suit $=4\times 715=2860$