Perms and Combs Help (1 Viewer)

[luo_ge]

Can i please get some help with this question. Perms and combs aren't really my strong point.

5. A television director is scheduling a certain sponsor’s commercials for an upcoming broadcast.
There are six slots available for commercials. In how many ways may the director
schedule the commercials
a) If the sponsor has six different commercials, each to be shown once?
b) If the sponsor has three different commercials, each to be shown twice?
c) If the sponsor has two different commercials, each to be shown three times?
d) If the sponsor has three different commercials, the first of which is to be shown three
times, the second two times, and the third once?

I can do a) but can't do the rest.

Thanks.

 

[pikachu975]

Do you have the answers?

 

[InteGrand]

Can i please get some help with this question. Perms and combs aren't really my strong point.

5. A television director is scheduling a certain sponsor’s commercials for an upcoming broadcast.
There are six slots available for commercials. In how many ways may the director
schedule the commercials
a) If the sponsor has six different commercials, each to be shown once?
b) If the sponsor has three different commercials, each to be shown twice?
c) If the sponsor has two different commercials, each to be shown three times?
d) If the sponsor has three different commercials, the first of which is to be shown three
times, the second two times, and the third once?

I can do a) but can't do the rest.

Thanks.

These are just standard Q's where we're arranging objects that have more than one of a kind, so we have to divide by factorials of the number of each kind. So the answers are:

b) 6!/(2!*2!*2!)

c) 6!/(3!*3!)

d) 6!/(3!*2!*1!).