Question

(i) Find the number of four letter word that can be formed from the letters of the word HISTORY. ( each letter to be used at most once)
(ii) How many contain both vowels?

Answer 1

1) letters total: 7.
word length =4...
So 7P4 = 7!/3! = 840.

ii) Choose both vowels.
Then we need to choose 2 more letters from the remaining 5. So 5C2 ways. Then permute all four letters.

So 5C2 × 4P4 = 240.