GRE Math Practice Data Analysis Question

**mishum2000** · 09-10-2005, 06:08 PM

Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row. In how many of those ways is Martha sitting in the middle?
How to solve this ?

I'm waiting for your replies,

Thanks,

Michael.

**priyankagre2005** · 09-10-2005, 06:18 PM

Ans: 24
There are total of 5 people (including martha). If martha sits in the middle, total people left to be arranged in a line are 4, who can arrange themselves in 4! ways.

**Hermione** · 09-10-2005, 06:32 PM

Agree with priyanka, but without doing the calculations....
there are five people and it is given that there are 120 combos, so martha will be in the middle 1/5 of the times, which is 24.

**mishum2000** · 09-11-2005, 12:36 PM

Thanks guys, the problem was indeed very simple. I was confused by the fact that Martha should sit in the middle. I guess the situation remains the same if Martha stays in any other place than middle.

**nihar** · 09-12-2005, 04:21 AM

can anybody por favor, el señor explain in detail .can't get it

**Hermione** · 09-12-2005, 05:17 PM

Originally Posted by nihar

can anybody por favor, el señor explain in detail .can't get it

Ok, see: martha and four of her friends go to a movie.
no of people: 5
total number of arrangements possible: 5! = 5*4*3*2*1 = 120
As there are totally five positions martha can occupy, the probability that martha will be in the middle is 1/5 and the number of arrangements in which this occurs is 1/5 * 120 = 24.