Problem Solving

ritumaheshwari02 wrote:Kate, Leonard, and 3 other schoolchildren are to be seated in a row of 5 seats facing their class. For how many of the possible arrangements of the 5 children in the 5 seats will either Kate or Leonard be seated in the middle seat?

A. 5
B. 10
C. 25
D. 32
E. 48

Another approach is to recognize that we can seat the 5 children in 5! ways (120 ways).

With all things considered equal, each person is equally likely to sit in the middle chair.
So, of those 120 arrangements, 1/5 will feature Kate in the middle, and 1/5 will feature Leonard in the middle.
In other words, 2/5 of the 120 arrangements will feature either Kate or Leonard in the middle seat.

2/5 of 120 is 48, so the correct answer is E

Cheers,
Brent

Bill@VeritasPrep wrote:

Brent@GMATPrepNow wrote:

ritumaheshwari02 wrote:Kate, Leonard, and 3 other schoolchildren are to be seated in a row of 5 seats facing their class. For how many of the possible arrangements of the 5 children in the 5 seats will either Kate or Leonard be seated in the middle seat?

A. 5
B. 10
C. 25
D. 32
E. 48

Another approach is to recognize that we can seat the 5 children in 5! ways (120 ways).

With all things considered equal, each person is equally likely to sit in the middle chair.
So, of those 120 arrangements, 1/5 will feature Kate in the middle, and 1/5 will feature Leonard in the middle.
In other words, 2/5 of the 120 arrangements will feature either Kate or Leonard in the middle seat.

2/5 of 120 is 48, so the correct answer is E

Cheers,
Brent

That's one of my favorite things about combinatorics questions. There are usually multiple good ways to solve a given problem, so it's more a matter of thinking your way through a problem then memorizing strict rules.

Agreed! In fact we could probably apply that sentiment to most GMAT math questions. There's almost always more than 1 approach that works.

Cheers,
Brent