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by topspin20 » Tue Aug 13, 2013 5:20 pm
Aunt Ella, Billy, Clyde, Dom, and Ean sit on a large park bench. Wherever Billy goes, he must always be next to Aunt Ella. How many possible ways can the five sit on the bench?

A) 12
B) 20
C) 48
D) 82
E) 120
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by Brent@GMATPrepNow » Tue Aug 13, 2013 6:13 pm
topspin20 wrote:Aunt Ella, Billy, Clyde, Dom, and Ean sit on a large park bench. Wherever Billy goes, he must always be next to Aunt Ella. How many possible ways can the five sit on the bench?

A) 12
B) 20
C) 48
D) 82
E) 120
One approach is to "glue" Billy and Aunt Ella together. This couple becomes 1 entity, so we now have just 4 entities:
1. Clyde
2. Dom
3. Ean
4. The Billy-Aunt-Ella combo

We can arrange these 4 unique objects in 4! ways (24 ways)
BUT the answer isn't 24.
Keep in mind that, for each of these 24 arrangements, we have 2 possible ways to seat Aunt Ella and Billy within their Billy-Aunt-Ella combo.

So, the total number of arrangements = [spoiler](24)(2) = 48 = C[/spoiler]

Cheers,
Brent
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by ganeshrkamath » Tue Aug 13, 2013 10:32 pm
topspin20 wrote:Aunt Ella, Billy, Clyde, Dom, and Ean sit on a large park bench. Wherever Billy goes, he must always be next to Aunt Ella. How many possible ways can the five sit on the bench?

A) 12
B) 20
C) 48
D) 82
E) 120
Billy = B
Ella = E
Possible cases:
B E _ _ _
E B _ _ _
_ B E _ _
_ E B _ _
_ _ B E _
_ _ E B _
_ _ _ B E
_ _ _ E B

So total number of possible ways = 3! * 8 = 48

Choose C

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