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?

Answer 1

The first 13 cards (all hearts) have
`13!` ways of being arranged. The remaining 39 have
`39!` ways of being arranged.

The total number of such arrangements is then
`13!39!`, or about
`1.27*10^(56)` arrangements.