Question

65. In how many ways can one permute the letters
of the word CONSTANT keeping two vowels together?
(A) 2500
(B) 2520
(C)1260
(D) 2560
​

Answer 1

Answer:

can do the same with OA.

So, total ways of arranging letters keeping vowels together = 2 (5!) = 240.

Our answer = 6! - 240 = 480.

Alternative method :

Let's use a logic that arranging 'n' things creates 'n+1' gaps.

If we arrange 4 consonants of a given word, 5 gaps will be generated. But there are only 2 vowels.

Ways of choosing gaps = 5C2.

Now, vowels & consonants can change their places in 2! & 4! ways respectively.

Total ways = 5C2 × 2! × 4!

= 10 × 2 × 24 = 480.

Note : If a given word has 2+ vowels, it's feasible to use a 2nd method.