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
Arrangements
This topic has expert replies
-
- Legendary Member
- Posts: 966
- Joined: Sat Jan 02, 2010 8:06 am
- Thanked: 230 times
- Followed by:21 members
- cans
- Legendary Member
- Posts: 1309
- Joined: Mon Apr 04, 2011 5:34 am
- Location: India
- Thanked: 310 times
- Followed by:123 members
- GMAT Score:750
8C5.
IMO C
IMO C
If my post helped you- let me know by pushing the thanks button
Contact me about long distance tutoring!
[email protected]
Cans!!
Contact me about long distance tutoring!
[email protected]
Cans!!
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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.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
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