Hello, Flay!

We have to "talk" our way through these problems . . .

There are 2 possible arrangements: .A queue has 4 boys and 4 girls standing in line.

Find how mant different arrangements are possible if;

a) The boys and girls alternate.

The four boys can be placed in 4! ways.

The four girls can be placed in 4! ways.

Therefore, there are: . ways.

Suppose the two girls are andb) 2 particular girls wish to stand together.

Duct-tape them together.

Note that there are 2 possible orders: .

Now we have seven "people" to arrange: .

. . and they can be arranged in ways.

Therefore, there are: . ways.

Duct-tape the four boys together.c) All the boys stand together.

. . Note that there are 4! possible orders.

Now we have five "people" to arrange.

. . There are ways.

Therefore, there are: . ways.

First of all, there are 8! possible arrangements.d) Find the probability that 3 particular people will be together

if the queue forms randomly.

Suppose the three people are

Duct-tape them together: .

. . Note that there are 3! orderings.

Now we have six "people" to arrange,

. . and there are 6! ways.

Hence, there are: . ways for to be together.

Therefore, the probability is: .