Correct Answer - Option 3 : 25200
Concept:
The number of ways to select r things out of n given things wherein r ≤ n is given by: \({\;^n}{C_r} = \frac{{n!}}{{r!\; × \left( {n - r} \right)!}}\)
Calculation:
Given: There are 7 consonants and 4 vowels
Here, we have to find how many word can be formed such that it has 3 consonants and 2 vowels.
No. of ways to select 2 vowels out of 4 vowels = \({\;^4}{C_2} \)
No. of ways to select 3 consonants out of 7 consonants = \({\;^7}{C_3} \)
∴ No. of words that can be formed which contains 3 consonants and 2 vowels = \({\;^4}{C_2} \) × \({\;^7}{C_3} \)
As we know that, \({\;^n}{C_r} = \frac{{n!}}{{r!\; × \left( {n - r} \right)!}}\)
⇒ \({\;^4}{C_2} \) × \({\;^7}{C_3} \) = 6 × 35 = 210
The no. of ways to arrange words containing 3 consonants and 2 vowels = 210 × 5! = 25200
Hence, option C is the correct answer.
