Question

Ahandofsevencards isdealt from adeck of 52 cards. (a) Howmanyhandsarepossible? (b) Howmanyhandsthatcontainexactly2diamonds arepossible? (c) Howmanyhandswith2diamondsand3spadesarepossible?

Answer 1

a. There are total 52 cards in a deck . We are drawing 7 cards out of them .

We can draw 7 cards from 52 in different ways.

Then total number of different possible hands is given by

= 133784560

b. Now we will choose 7 cards out of which 2 is diamond.

There are total 13 card of diamond. So we will choose 2 from this 13 cards in ways and  remaining 5 card from remaining (52-13) = 39 cards in ways.

Number of different hands that contains exactly 2 diamonds is = × = 44909046

c. There are 13 diamonds and 13 spades in a deck of cards. So we can choose 2 diamonds from 13 in ways and 3 spades from 13 in ways. And remaining (7-2-3)=2 cards from the remaining (52-13-13) =26 cards in waya.

So Number of different hands contains 2 diamonds and 3 spades is =×× = 7250100