GMAT Prep From Platinum GMAT

GMAT Prep Materials

Announcement

Check out our latest blog post about The Best GMAT Books for Studying on Your Own.

About Us

Platinum GMAT Prep provides the best GMAT preparation materials available anywhere, enabling individuals to master the GMAT and gain admission to any MBA program. We also provide hundreds of pages of free GMAT prep content, including practice questions, study guides, and test overviews.

rss GMAT Practice Question (One of Hundreds)
There are five empty chairs in a row. If six men and four women are waiting to be seated, what is the probability that the seats will be occupied by two men and three women?
Correct Answer: B
The probability of seating two men and three women in the empty chairs = (total number of ways of choosing 2 men out of 6 and 3 women out of 4)/ (number of ways of seating five people out of ten).
  1. This is a combination-probability problem. To solve this we will need to find out the number of ways we can choose 2 men out of 6 and 3 women out of 4 to sit in the chair.
  2. Next, we note that the probability of seating two men and three women in the empty chairs is:
    (number of ways of choosing 2 men and 3 women)/ (number of ways of seating five people out of ten).
  3. The total number of ways of choosing five people to sit out of a total of ten (six men + four women) is given by:
    10C5 = 10!/([10-5]!5!)
    = (10*9*8*7*6)/[10-5]!
    = (10*9*8*7*6)/5!
    = 252
  4. Now we want the seats to be taken by 2 men and 3 women.
    I. The number of ways to choose 2 men out of six to occupy the seat is given by:
    6C2 = 6!/4!*2! = 15
    II. The number of ways to choose 3 women out of 4 to sit is given by:
    4C3 = 4!/3!*1! = 4
  5. Using the multiplication principle, the total number of ways to select two men and three women is:
    15*4=60
  6. The probability is thus = 60/252
    = (12*5)/(12*21)
    = 5/21. Hence the correct answer choice is B