Question

How many ways can 3 boys and 2 girls stand in a row so that the two girls are not next to each other? 60,72, 90, 100

Answer 1

Explanation:

I think 6 ways is the correct answer

Answer 2

72

Explanation:

For now, let's just distinguish between boys and girls.

Boy = X

Girl = x

There are 6 ways of placing the boys and girls so that the girls are not next to each other.

XXxXx

XxXXx

xXXXx

XxXxX

xXXxX

xXxXX

Now let's look at one of those patterns while distinguishing between the individual boys and girls by having a different symbol for each.

Boys: A, B, C

Girls: a, b

Let's use just the first pattern above, XXxXx.

ABaCb

ACaBb

BAaCb

BCaAb

CAaBb

CBaAb

ABbCa

ACbBa

BAbCa

BCbAa

CAbBa

CBbAa

For the first pattern of the 6 different patterns on top, there are 12 ways of placing the boys ad girls. Since there are 6 of the patterns on top, the total number of ways is

6 * 12 = 72

Answer: 72