Question

In how many ways can a standard deck of 52 cards be shuffled so that the first 13 cards are all spades (there are only 13 spades in the deck)?

Answer 1

We want to shuffle a deck of cards such that first 13 cards are all spades. For this, we use a way that we will keep all spade together and shuffle them and then we will shuffle all remaining cards together and shuffle them then we will put spades on the top.

All 13 spades can be shuffled in ways

Remaining 39 cards can be shuffled in ways

Now the total number of ways of shuffling the cards such that first 13 cards are spades.