What have you tried on any of these?
Have you done any work on them?
The answer to part c is: 2(3!)(3!).
Hi to all
I have few short questions if you would like to look at them
a)in how many ways can 3 boys and 3 girls sit in a row?
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
c)in how many ways if only the boys must sit together?
d)in how many ways if no two people of the same sex are allowed top sit together?
Thank you
Actually parts b & c have the same numerical answer.
The reasons for that are entirely different.
You may be reading “if only” as “only if”. They are not the same!
In the future, if you post your answers we will know that you are not just on a fishing expedition to see if someone will do your work for you.
Hello, mauro21pl!
With six people, there are: . ways.a) In how many ways can 3 boys and 3 girls sit in a row?
There are two arrangements of the genders: . orb) 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?
In each, the three boys can be ordered in ways
. . and the girls can be ordered in ways.
Therefore, there are: . ways.
Duct-tape the boys together.c) In how many ways if only the boys must sit 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.
Since the boys and girls must alternate,d) In how many ways if no two people of the same sex are allowed to sit together?
. . 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.