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

Answer:

Probability to pick 4 tiles which spell CATS will be $\frac{1}{70}$.

Step-by-step 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 = $^{8}C_{4}$

= $\frac{8!}{4!(8-4)!}$

= $\frac{8!}{4!\times 4!}$

= $\frac{8\times 7\times 6\times 5\times4!}{4!\times 4!}$

= $\frac{1680}{24}$

= 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

= $\frac{1}{70}$

Therefore, probability to pick 4 tiles which spell CATS will be $\frac{1}{70}$.