Question

52 cards choose 4

3 are the same suit and 1 is any other suit

Answer 1

There are 4 suites of cards in the deck each with 13 cards. 4 cards are to be selected from the deck of 52 cards. The required event can be written in steps as:

Step 1: 1 suite is chosen from 4 suites. This can be done in 4C1 = 4 ways.

Step 2: Then out of the 4 cards, 3 cards are chosen this can be done jn 4C3 = 4 ways.

Step 3: 3 cards will be from the 13 cards of the same deck selected in step 1. This can be done in 13C3 = 13!/(3!*10!) = 286 ways.

Step 4: the remaining 1 card is selected from the other 3 decks, that is from the remaining (52-13)=39 ways. This can be possible in 39C1= 39 ways.

Thus the required number of ways = product of number of ways in which each of the 4 steps can be done = 4*4*286*39= 178464.

Answer is 178464.

Hope the solution helps. Thank you.