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 belong to four different suits.

Answer 1

Total No.of cards to be chosen no.of ways.

Diamond 13 1 $13c_1$

spade 13 1 $13c_1$

Heart 13 1 $13c_1$

Club 13 1 $13c_1$

Since they are the same case,

So,we can multiply the number of ways.

Hence the required no.of ways choosing

four cards form each suit= $13c_1\times 13c_1\times 13c_1\times 13c_1$

$=(13c_1{)}^4$

$=(\frac{13!}{11(13-1)!}{)}^4$

$=\left({\frac{13\times 12!}{12!}}^4\right)$

$=(13{)}^4$

$=28561$ ways.