Question

in how many ways can the letter of the word intermediate be arranged so that the vowels occupy even places

Answer 1

Number of letters in the word = 12

Number of vowels in the word = 6

⇒ Number of non vowels letter in the work = 12 - 6 = 6

Find the number of combinations possible:

In between two letters is a vowels

Number of ways 6 x 6 x 5 x 5 x 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 = 518,400

Answer: There are 518,400 possible combinations

Answer 2

Answer:

21,600

Step-by-step explanation:

Given : in how many ways can the letter of the word intermediate be arranged so that the vowels occupy even places

 Number of ways to arrange the vowels

          I N T E R M E D I A T E

There are 12 letters 6 odd and 6 even.

 Vowels: Now 6 positions to be filled taking 6 at time.

 Therefore total permutation = 6 P 6

      so formula is n ! / (n - r)! = 6 ! / (6 - 6)! = 6!

 Therefore total combination is 6! / 3! 2! = 60 (because E is repeated 3 times and I is repeated 2 times).

Now coming to consonants or odd places, total number of ways in which odd positions can be filled is 6! /2! = 360(since T is repeated twice)

So total number of places will be 360 x 60 = 21,600