Question

If we draw 5 cards out of a deck of 52 cards, what is the probability that we have 3 cards from the same suit.

Answer 1

Answer:0.5176

Explanation:

Given

We need to draw 5 cards out of 52 cards

So no of ways of choosing 5 cards out of 52 is
`^(52)C_(5)`

Now to choose 3 cards of same suit

First we have to choose 1 suit out of 4 which can be done in
`^4C_1` ways

Now choosing 3 out of 13 cards is
`^(13)C_3`

and remaining two cards can be chosen in
`^(49)C_2`

So total no of ways are
`=^4C_1* ^(13)C_3* ^(49)C_2`

So probability
`=(^4C_1* ^(13)C_3* ^(49)C_2)/(^(52)C_(5))`

`P=(4* 26* 11* 49* 24)/(2598960)`

`P=0.5176`