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

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.

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

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.