From 8 consonants along with 5 vowels, how many words can be formed of 3 consonants and 2 vowels?
From 8 consonants along with 5 vowels, how many words can be formed of 3 consonants and 2 vowels? Correct Answer 67200
Given:
Out of 8 consonants and 5 vowels, words of 3 consonants and 2 vowels to be formed
The concept used:
Permutations and Combinations
Formula used:
nCr = n! /r! (n - r)!
n! = n × (n - 1) × (n - 2) × (n - 3) × (n - 4) ... × 1
Calculation:
Number of ways of selecting 3 consonants from 8 is 8C3
Number of ways of selecting 2 vowels from 5 is 5C2
Number of ways of selecting 3 consonants from 8 and 2 vowels from 5 is 8C3 × 5C2
⇒ {(8 × 7 × 6) / 3 × 2 × 1} × {(5 × 4)/2 × 1}
⇒ 56 × 10
⇒ 560
It means we can have 560 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves
⇒ 5!
⇒ 5 × 4 × 3 × 2 × 1
⇒ 120
Total number of words formed will be
⇒ 560 × 120
⇒ 67200
∴ Required number of ways is 67200