Question

Out of 25 consonants and 5 vowels how many words can be formed each consisting of 2 consonants and 3 vowels?

Answer 1

Hint: Since we need to select a few items from a group of items the concept of combinations is used.

Complete step-by-step answer:
In this question you have 25 consonants and 5 vowels.
So,
Two consonants from 25 can be chosen in ${}^{25}{C_2}$ ways and
Three vowels from 5 can be chosen in ${}^5{C_3}$ ways and
5 letters can be arranged in $5!$ ways
So, Number of words that can be formed is = ${}^{25}{C_2}.{}^5{C_3}.5! = 360000$

Note: This question is based on combinations and can be easily solved but you must remember to take into consideration the arrangement of the letters.