How many words of 2 consonants and 2 vowels can be formed from 5 consonants and 4 vowels?

How many words of 2 consonants and 2 vowels can be formed from 5 consonants and 4 vowels? Correct Answer 1440

Given:

Number of consonants = 5

Number of vowels = 4

Formula used:

ⁿC_r = n!/

Calculation:

Number of ways selecting 2 consonants = ⁵C₂

⇒ Number of ways selecting 2 consonants = 5!/

⇒ Number of ways selecting 2 consonants = (5 × 4 × 3!)/(2 × 1 × 3!)

⇒ Number of ways selecting 2 consonants = 10

Number of ways selecting 2 vowels = ⁴C₂

⇒ Number of ways selecting 2 vowels = (4 × 3)/(2 × 1)

⇒ Number of ways selecting 2 vowels = 6

Number of ways selecting 2 consonants and 2 vowels = 10 × 6

⇒ Number of ways selecting 2 consonants and 2 vowels = 60

Number of ways of arranging 4 letters among themselves = 4 × 3 × 2 × 1

⇒ Number of ways of arranging 4 letters among themselves = 24

Required number of ways = 60 × 24

⇒ Required number of ways = 1440

∴ The total number of ways is 1440.