Out of 7 consonants and 4 vowels. how many words of 3 consonant and 2 vowels can be formed?

Explanation

Total number of ways of choosing (3 consonants out of 7) and (2 vowels out of 4)
`=(.^(7)C_(3)xx.^(4)C_(2))=((7xx6xx5)/(3xx2xx1)xx(4xx3)/(2xx1))=210`.
Number of groups, each containing 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging 5 letters amongst themselves
`=5! = (5xx4xx3xx2xx1)=120`.
Hence, the required number of words `= (210xx120)=25200`.