Question

A poker hand, which consists of 5 cards, is drawn from an ordinary deck. What is the chance of the following events?

The first 2 cards and the last 2 cards are aces?

Answer 1

The number of possible poker hands:

⁵²c₅ = 52!/5! × 47!

= 2,598,960

If we remove 4 aces from a deck of card we are left with 48 cards.

So, first and last two cards are aces. And we can place the rest 48 cards one by one into the middle of aces.

So number of ways the middle number can change = 48

And those four aces can change their places within themselves.

So number of ways the aces can change their places = 4! = 24

Number of such ways possible = 24 × 48 = 1152

Probability of this event = 1152/2598960 = 0.00044