Question

Suppose Roger has 4 green tennis balls and 5 red tennis balls. All the balls of
the same colour are identical. In how many ways can Roger arrange these 9
balls in a line so that no two green balls are next to each other and no three
red balls are together?
(B) 9
(C) 11
(D) 12
(A) 8​

Answer 1

Given:

4 green tennis balls and 5 red tennis balls

To find:

Ways in which Roger can arrange the 9 balls in a line so that no two green balls are next to each other and no three red balls are together.

Solution:

• Let us consider the arrangement -

____R____R_____R_____R_____R____

• Here, 4 green balls can be arranged in 6 places as per the above arrangement.

• Thus the ways will be = ⁶C₄

• Also, in some of the arrangement 3 red balls comes together and those arrangements can't be taken.

• These 3 arrangements are GRRRGRGRG, GRGRGRRRG, and GRGRRRGRG.

• Thus, the ways will be =  ⁶C₄  - 3

                                              = 12

• Therefore, the total no. of ways will be 12.