Modern Math

Permutation & Combination

Medium

Out of 7 different consonants and 4 different vowels, how many words (not necessarily meaningful) of 4 consonants and 2 vowels can be formed?

151200

210

720

142500

✅ Correct Option: 1

Number of ways of selecting (4 consonants out of 7) and (2 vowels out of 4) = $^7C_4 \times ^4C_2 = 35 \times 6 = 210$

Number of groups, each having 4 consonants and 2 vowels = 210.

Each group contains 6 letters.

Number of ways 6 letters can arrange themselves = $6! = 720$

$\therefore$ Required number of ways = $(210 \times 720) = 151200$ .

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Solution

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