jack0997 wrote:
There are 10 male and 8 female dancers in a club. If the club is to form two groups, each having 1 male and 1 female dancer, in how many ways can it be done?
(A)143
(B) 160
(C) 1,260
(D) 2,520
(E) 5,040
The number of ways to select the first group of 1 male and 1 female dancers is 10 x 8 = 80. The number of ways to select the next group is 9 x 7 = 63. Notice that when we multiply 80 and 63, we will have counted each pair of groups twice: If AB is one group and CD is another group; we first count AB as the first group and CD as the second group and then, we count CD as the first group and AB as the second group, but these pairs of groups actually represent one of the possibilities. Thus, we need to divide the product by 2. Therefore, the total number of ways to select the 2 groups is 80 x 63 x 1/2 = 2,520.
Answer: D
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.