How many distinct ways are there of ordering a deck of 52 ca

How many distinct ways are there of ordering a deck of 52 cards such that all hearts occur before any other card? (That is, the first 13 cards are all hearts.)

Solution

There are total 13 Hearts in a pack of 52 cards.

For the first 13 cards to be Hearts, the next 39 cards should be Clubs, Spades and Diamonds.

Number of ways to arrange first 13 cards as Hearts = 13!

Number of ways to arrange next 39 cards = 39!

Thus total number of ways to order a deck of 52 cards such that first 13 cards are all heart = 13! X 39!