Suppose you select a card from a standard deck of 52 playing cards.?

Question

In how many ways can the selected card be: 1. A red card? 2. A heart? 3.a queen and a heart? 4. A queen or a heart? 5.a queen that is not a heart? Im in desperate need of help. I would be able to do it if it was probability but its asking how many ways and i'm totally lost.

Answer 1

1. Among 52 playing cards there are 26 red cards

   So, there is a possibility of 26 times to select a red card

    26

2. Among 52 playing cards there are 13 hearts

   So, there is a possibility of 13 times to select a heart

   13

3. There is only one possibility to select a queen and a heart

   01

4. There is a possibility of 16 times

   16

5. There is a possibility of 3 times to select a queen that is not a heart

   03

Answer 2

There are 52 playing cards in a deck.

Out of 52, there are 26 red cards and 26 black cards.

Out of 52, there are 13 spades, 13 diamonds, 13 clubs and 13 hearts.

There are 4 sets of numbers i.e., ace, 2 to 10, jack, king and queen.

1) A red card can be selected in 26C₁ = 26 ways.

2) A heart can be selected in 13C₁ = 13 ways.

3) A queen can be selected in 4C₁ ways.

A heart can be selected in 13C₁ ways.

A queen and heart can be selected in 4C₁ * 13C₁= 4 * 13 = 52 ways.

4) A queen or heart can be selected in 4C₁ + 13C₁= 4 + 13 = 17 ways.

5) There are 4 queens with 4 symbols - heart, spade, diamond and club.

A queen that is not a heart can be selected in 3 ways.