Question 49

Mathematics Permutation and Combination Medium

Out of 5 consonants and 4 vowels, how many words of 3 consonants and 3 vowels can be made?

(A) 40
(B) 80
(C) 20
(D) 240
View Dynamic Solution & Explanation
Correct Solution: Option A

Step-by-step Solution:

Solution

We are given 5 consonants and 4 vowels. We need to form words with 3 consonants and 3 vowels.

Step 1: Choose 3 consonants out of 5:

\(\binom{5}{3} = 10\)

Step 2: Choose 3 vowels out of 4:

\(\binom{4}{3} = 4\)

Step 3: Arrange the selected 6 letters (3 consonants + 3 vowels) in a word:

\(6! = 720\)

Note: If the question assumes only selection then the correct answer is

\(10 \times 4 = 40\)

Answer: Option A with resepect to selection