Question

Find the number of four letter word that can be formed from the letter of the word $HISTORY$ .(each letter to be used atmost once)
How many contain both vowels?

Answer 1

total number of different types of letters = 7

we have to make a 4 letter word that contains both vowels ,

no. of ways in which other two letter can be filled = $5\times 4$ , as two are filled with vowels,

two vowels will permutate in 4! ways

no. of ways it can be done = $1\times 5\times 4\times 4!$

=$24\times 20=480ways$