Question

In how many ways can the letters of the word constant' be arranged such that the word always starts with a vowel?

Answer 1

Answer:

The letters of the word 'CONSTANT' can be arranged in total of 2520 ways to have started with a vowel every time.

Explanation:

The word 'CONSTANT' has 8 letters altogether. Let us assume, there are two vowels, O and A, so we keep them aside together as 1 letter. Then the total number of letters are 8-1=7

So, the letters of the word can now be arranged in 7! ways.

Now, the letter N is repeated twice in the word. So they can be arranged in 2! ways. We divide 7! by 2!

Therefore, 7!/ 2!

Also, the letter T is repeated twice in the word. So they can be arranged in 2! ways. We divide 7! by 2! again. That makes it,

7!/(2!×2!)

The assumed 1 letter of vowels 'OA' can be arranged in 2! ways. So we need to multiply 2! with 7!/(2!×2!)

Therefore, {7!/(2!×2!)}×2!

So the equation is, {(7×6×5×4×3×2×1 ) / (2×2)} × 2

=> 2520