Discrete Math ordering 52 card deck question How many distin

Discrete Math ordering 52 card deck question

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

13 heart cards can be arranged in 13 ! ways in first 13 positions and remaining 39 positions will be filled by 39 cards that can be arranged in 39! ways. So total ways of arranging 13 all hearts together before remaining 39 cards

= 13! x 39!

= 6227020800 (39!)

Answer