Question

how many 5 card hands have no spades ?

Answer 1

In a deck of card there are 52 cards ,so 5 cards can be choosen from deck in ⁵²C₅ ways.

Now we have to find the probability that 5 choosen cards contain no spades . Therefore the 5 cards can be choose out of non-spade cards . In a deck there are 13 spade cards.

So number of non -spade cards =52-13=39 cards.

Out of 39 cards ,5 card can be choosen in ³⁹C₅ ways.

Thus ,P( 5 cards hand have no spades)= ³⁹C₅  / ⁵²C₅

(39)!/((34)! (5)!)

= --------------------------------------

(52)!/((47)! (5)!)

= 575757/ 2598960

= 0.22153361