Question

A group of seven kids line up in a random order. Each ordering of the kids is equally likely. There are three girls and four boys in the group. What is the probability that all the girls are ahead of all the boys

Answer 1

Using the arrangements formula, it is found that there is a 0.0286 = 2.86% probability that all the girls are ahead of all the boys.

What is the arrangements formula?

The number of possible arrangements of n elements is the factorial of n, that is:

$A_n = n!$.

The total number of outcomes is the arrangement of 7 elements, hence:

T = 7! = 5040.

The desired number of outcomes is all girls(3!), then all boys(4!), hence:

D = 3! x 4! = 6 x 24 = 144.

Hence, the probability is:

p = D/T = 144/5040 = 0.0286.

There is a 0.0286 = 2.86% probability that all the girls are ahead of all the boys.

More can be learned about the arrangements formula at brainly.com/question/24648661