four letters are chosen at from the letters of the word TAILORED .find the probability of getting a T and three vowels.
Choose three vowels: $\dbinom{4}{3}$ ways. Choose the $t$: 1 way.
By the product principle, there are 4 ways to choose a T and three vowels.
Total number of ways to choose four letters from TAILORED: $\dbinom{8}{4}$
Probability: $\dfrac{4}{\dbinom{8}{4}} = \dfrac{2}{35}$