Exercise 29 Page 898

When calculating probability, we are comparing the number of favorable outcomes to the number of possible outcomes. Let's figure out each of those numbers one at a time and then use the Probability Formula.

Possible Outcomes

There are 2 girls and 2 boys in the band, and therefore the band has 4 members. They all line up in random order, so the number of all possible outcomes is 4!. Possible outcomes: 4! Let's evaluate this expression.

4!

Write as a product

4* 3* 2* 1

Multiply

Multiply

24

Favorable Outcomes

Let's consider the given situation. We want to know the probability that a girl will be at each end of the row if they line up in random order.

Since both members of each group are distinguishable, we need to consider their permutations as well. There are 2! ways to permute girls and 2! ways to permute boys. We can use the Fundamental Counting Principle to find the number of favorable outcomes. cccc Number of Ways & & Number of Ways to Permute Boys & & to Permute Girls 2! & * & 2! Let's simplify the above expression to find the number of favorable outcomes.

2!* 2!

2!=2

2 * 2

Multiply

Multiply

4

Probability

Finally, we can calculate the desired probability.

P=Favorable Outcomes/Possible Outcomes

SubstituteValues

Substitute values

P = 4/24

ReduceFrac

a/b=.a /4./.b /4.

P = 1/6

This corresponds to option C.