Arrangements

shankar.ashwin wrote:A problem similar to what I posted earlier

In how many ways can 5 brothers sit in 8 chairs so that an elder brother is always to the right of a younger brother. (Assume there are no twins)

A) 4
B) 8
C) 56
D) 60
E) 120

To elaborate on cans' approach, we can see that the seating order of the brothers is fixed - an elder brother is always to the right of a younger brother.

So, if there were 5 chairs in this question, there would be only one possible arrangement (youngest, second youngest, middle guy, second oldest, oldest)

Now this question features 8 chairs, so it really comes down to: in how many different ways can we select 5 chairs for the brothers to sit in?

Well, since the order in which we select the chairs does not matter (e.g., selecting chairs 1, 3, 4, 7, 8 is the same as selecting chairs 7, 8, 1, 4, 3), this is a combination question.

We can select 5 chairs (from 8 chairs) in 8C5 ways (56 ways)

Cheers,
Brent