Out of 7 consonants and 4 vowels, how many 5-letter words consisting of 3 consonants and 2 vowels can be formed?

Problem restatementChoose 3 consonants and 2 vowels and arrange the 5 chosen letters in all possible orders.

Given data

• Consonants available = 7.
• Vowels available = 4.
• Word length = 5 (with 3 consonants + 2 vowels).

Concept/ApproachIndependent selection followed by permutations: choose letters first, then arrange them (all distinct).

Step-by-step calculation Choose consonants: C(7, 3) = 35 Choose vowels: C(4, 2) = 6 Arrange 5 letters: 5! = 120 Total = 35 × 6 × 120 = 25200

Verification/AlternativeThe multiplication principle applies: selections are independent and letters are distinct.

Common pitfalls

• Multiplying by 5! before selecting the letters, or double-counting arrangements.

Final Answer25200