Hello, mauro21pl!

Quote:

a) In how many ways can 3 boys and 3 girls sit in a row?

With six people, there are: . ways.

Quote:

b) In how many ways can 3 boys and 3 girls sit in the row

if the boys and the girls are each to sit together?

There are two arrangements of the genders: . or

In each, the three boys can be ordered in ways

. . and the girls can be ordered in ways.

Therefore, there are: . ways.

Quote:

c) In how many ways if only the boys must sit together?

Duct-tape the boys together.

Then there are four "people" to arrange. .There are arrangements.

For each arrangement, the three boys can be ordered in ways.

Therefore, there are: . ways.

Quote:

d) In how many ways if no two people of the same sex are allowed to sit together?

Since the boys and girls must alternate,

. . there are two arrangements: . or

For each arrangement, the three boys can be ordered in ways

. . and the three girls can be ordered in ways.

Therefore, there are: . ways.