Question

You have 8 scrabble tiles A, B, C, D, R, S, T, U in a bag. You reach in and randomly pick four of these tiles. What is the probability that you will be able to spell the word CATS with the tiles you picked?

Answer 1

Probability to pick 4 tiles which spell CATS will be
`(1)/(70)`.

Explanation:

We have 8 scrabble tiles A, B, C, D, R, S, T, U in a bag.

Probability to pick 4 tiles C, T, A, and S out of 8 tiles =
`^(8)C_(4)`

=
`(8!)/(4!(8-4)!)`

=
`(8!)/(4!* 4!)`

=
`(8* 7* 6* 5*4!)/(4!* 4!)`

=
`(1680)/(24)`

= 70

So we can choose C, T, A and S tiles in 70 different ways but the probability to pick 4 tiles which spell CATS will be

=
`(1)/(70)`

Therefore, probability to pick 4 tiles which spell CATS will be
`(1)/(70)`.