#2 doesn't make any sense. It says "vowels have to occupy the even positions" but there are not enough vowels to occupy the even positions. This is where the 4 comes in.

First, if you assume that the vowels occupy slot numbers 2, 4 and 6, then that leaves slot 8 open for a consonant.

The consonant's can be arranged in 5! ways, and the vowels in 3! ways. Together, that would be 120 * 6 = 720. But, that is assuming that the vowels occupy only slot #2, 4 and 6. Now, those vowels can be arranged in 3 of the 4 available slots. This is the same as selected 3 out of 4, which is also the same as selecting 4 (remember that in selecting 3, you're selecting 1 that is left out) This means that for any combination of placement for vowels, multiply that number by 4 and you get the number total.

Example: Vowels = O, U, E

2=0, 4=U, 6=E 8={Non-vowel}

In the same order of OUE, you could have 2={non vowel} 4=O 6=U 8=E. Same order, but different combination possibility.

So 4 * 720 accounts for the fact that vowels can be placed in any 3 of the 4 open "even" spots. Hope this helps.

srini123 wrote:

On how many ways can the letters of the word "COMPUTER" be arranged?

1. M must always occur at the third place

2. Vowels occupy the even positions.

Ans 1)

Ans 2)

Someone please explain 2, I understand 1

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J Allen Morris

**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.