perms and combs question (1 Viewer)

[-s-]

The question:

The answer is 6!/2! * 7C4 * 4!/3! = 50400. Somebody please explain how to arrive at this answer, thanks.

 

[InteGrand]

The question: View attachment 33357

The answer is 6!/2! * 7C4 * 4!/3! = 50400. Somebody please explain how to arrive at this answer, thanks.

Word: SUTHAHARAN.

If no two vowels are together, we essentially have:

* S * T * H * H * R * N *,

where we place the vowels each in one of the "*" spots above. It is easy to see that the configuration will have no two vowels apart if and only if the arrangement is like above.

First we arrange the relative positions of the consonants listed above, which is done in 6!/2! ways.

Then, we place the vowels U, A, A, A into the seven eligible "*" positions. This can be done in (7C4)*4 ways (choose the positions in 7C4 ways, then order U,A,A,A, which is done in 4 ways, or equivalently 4!/3!).

So the answer is 6!/2! * (7C4) * 4.

 

[ProdigyInspired]

So the answer is 6!/2! * (7C4) * 4!/3!.

beat me to it i was still typing