Question

4 cards are selected from a pack of 52 playing cards how many of the selections have all four cards of different suit and different denomination

Answer 1

Answer:

13 × 12 × 11 × 10 = 17160

Step-by-step explanation:

As there are four cards selected and there are four suits, there must be exactly one card from each suit.

There are 13 choices for the club.

To have a different denomination from the club, there are 12 choices for the diamond.

To have a different denomination from both the club and the diamond, there are 11 choices for the heart.

To have a different denomination from the other three cards, there are 10 choices for the spade.

In total, there are

13 × 12 × 11 × 10 = 17160

selections in which the cards are all of different suit and different denomination.