Answer:
Probability to pick 4 tiles which spell CATS will be [tex]\frac{1}{70}[/tex].
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 = [tex]^{8}C_{4}[/tex]
= [tex]\frac{8!}{4!(8-4)!}[/tex]
= [tex]\frac{8!}{4!\times 4!}[/tex]
= [tex]\frac{8\times 7\times 6\times 5\times4!}{4!\times 4!}[/tex]
= [tex]\frac{1680}{24}[/tex]
= 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
= [tex]\frac{1}{70}[/tex]
Therefore, probability to pick 4 tiles which spell CATS will be [tex]\frac{1}{70}[/tex].
