Thread: I need help in Permutations and Combinations

A theatre company consisting of 6 players is to be chosen from 15 actors. How many selections are possible if the company must include Mrs. Jones?

Note: The formula for "combinations of "n" different objects taken "r" at a time is

nCr = n!/(n-r)!r!




I have the answer down as (1 C 1) x (15 C 5). The answer in the workbook says it's (1 C 1) x (14 C 5).

Question: Why is it 14, and not 15 for the second C formula?

My understanding is this: there's 15 actors altogether. 1C1 comes from Mrs. Jones. That means there's 5 spots remaining but aren't there still 15 actors left that could be chosen? That would make it (15 C 5) but why does the answer say it's 14.

Originally Posted by garybeck1017

A theatre company consisting of 6 players is to be chosen from 15 actors. How many selections are possible if the company must include Mrs. Jones?
I have the answer down as (1 C 1) x (15 C 5). The answer in the workbook says it's (1 C 1) x (14 C 5).

If we remove Mrs. Jones from the group that leaves only 14.

Originally Posted by Plato

If we remove Mrs. Jones from the group that leaves only 14.

But why? Wait, are you saying Mrs. Jones counts as an actor? (a female's role as an actor is called actress). I feel stupid.

Originally Posted by garybeck1017

But why? There's still 15 actors to choose from.

No indeed.
The company has 15 members, one of which is Mrs. J.
Choose her how many are left?

Originally Posted by Plato

No indeed.
The company has 15 members, one of which is Mrs. J.
Choose her how many are left?

I think the workbook made an error. Mrs. Jones is actually Mr. Jones. Then that makes sense.

In the twenty-first century it seems safe to assume that the word ‘actor’ is gender neutral.
This is certainly true of the plural.
We don’t want to be sexist do we?