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 begin with $T$ & end in a vowel?

Answer 1

total number of different types of letters = 7

we have to make a 4 letter word begin with T and end with vowel ,

no. of ways in which first letter can be filled = 1

no. of ways in which last letter can be filled = 2

left letters=5

no. of ways it can be done = $1\times 5\times 4\times 2$

=$2\times 20=40$