How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?

A. ¹⁶C₇ × 7!

B. ¹²C₄ × ⁴C₃ × 7!

C. ¹²C₃ × ⁴C₄

D. ¹¹C₄ × ⁴C₃

Answer: Option B

Solution(By Examveda Team)

4 consonants out of 12 can be selected in,
¹²C₄ ways.
3 vowels can be selected in ⁴C₃ ways.
Therefore, total number of groups each containing 4 consonants and 3 vowels,
= ¹²C₄ × ⁴C₃ Each group contains 7 letters, which can be arranging in 7! ways.
Therefore required number of words,
= ¹²C₄ × ⁴C₃ × 7!