Question

In how many ways can 4 cards be selected from a pack of 52 cards so as to include at least one diamond card?​

Answer 1

Answer:

We are given a deck of 52 cards and 4 cards drawn.

Case I: All the cards are of same suit—

Now first of all we have to select one suit among 4.

This can be done in C(4,1)

Now select 4 cards from the already selected suit, this can be done in C(13,4)

Hence the answer is 4*13*12*11*10/(24)

= 2860

Therefore to choose 4 cards of the same suit we have 2860 ways.

Case II: All cards are of different suit:—

C(13,1)*C(13,1)*C(13,1)*C(13,1)

= (C(13,1))^4

= 13^4

= 28561.

Therefore to choose 4 cards from a deck of 52 cards of which all the 4 belongs to different suits, there are 28561 ways.

Answer 2

Step-by-step explanation:

no of diamond cards in a pack of cards =13

no. cards which are not diamond =52-13=39

at least one diamond = total-none of diamonds

no of ways you can pick 4 cards from 52 cards = 52c4

no. of ways of picking 4 cards from non diamond cards = 39c4

52c4-39c4