From 4 vowels and 8 consonants, how many words can be formed using 2 vowels and 3 consonants?

From 4 vowels and 8 consonants, how many words can be formed using 2 vowels and 3 consonants? Correct Answer 10080

Given that, 2 out of 4 vowels and 3 out of 8 consonants. So, (nCr * nCr). Where nCr = n! / r!(n – r)!. (4C2 * 8C3) = (4! / 2!(4 – 2)! * 8! / 2!(8 – 3)!) = (4 * 3 * 2!) / (2! * 2!) * (8 * 7 * 6 * 5!) / (4! * 5!)). (6 * 14) = 84. Number of words, each having 2 vowels and 3 consonants = 84. Each word contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 120. Required number of ways = (84 * 120) = 10080.