Question

An ordinary deck of playing cards contains 52 cards, 26 red and 26 black. If a card is dealt to each of 2 players,.

Find in how many different ways this can be done if the following occur.
a. both cards are red. _____ ways
b. both cards are black _____ways
c. one card is black and the other is red. ________way

Answer 1

(a)650 ways

(b)650 ways

(c)676 ways

Explanation:

There are 26 red and 26 black cards.

If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.

(a)Both cards are red

If both cards are red:

The first red card can be dealt in 26 ways.

The second red card can be dealt in 25 ways.

Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways

(b)Both cards are black

If both cards are black:

The first black card can be dealt in 26 ways.

The second black card can be dealt in 25 ways.

Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways

(c)One card is black and the other is red.

The red card can be dealt in 26 ways.

The black card can be dealt in 26 ways.

Therefore: Both cards can be dealt in: 26 X 26 = 676 ways