Question

How many words can be formed by using letters of the word trapezium' taking 2 vowels and 3 consonants?

Answer 1

TRAPEZIUM

Vowels = A, E, I, U

Constants = T, R, P, Z, M

Words that can be formed:

In the given word  TRAPEZIUM , all the letters are distinct and in total there

are 4 vowels and 5 consonants in this word.

2 vowels out of 4 vowels can be selected in 4C2 ways.

3 consonant out of 5 consonants can be selected in 5C3 ways.

So, 2 vowels and 3 consonants can be selected in 4C2*5C3 ways

    = 6*10 = 60.

Total number of ways , in which we can select 2 vowels and 3 consonants

are 60

These selected 5 letters(2 vowels and 3 consonants) can be arranged

amongselves in 5! ways = 120

Hence total number of words that can be formed = 120*60 = 7200

Hope, it helped !