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 of them begin & end in a consonant?

Answer 1

total number of different types of letters = $7$

no. of consonants = $5$

we have to make a $4$ letter word ,

first letter can be filled in $5$ ways

last can be filled in $4$ ways

now , left letters = $5$

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

=$16\times 25=400ways$