I need help in Permutations and Combinations

May 2010
3
0
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.
 
Last edited:

Plato

MHF Helper
Aug 2006
22,472
8,642
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.
 
May 2010
3
0
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.
 
Last edited:
May 2010
3
0
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.
 

Plato

MHF Helper
Aug 2006
22,472
8,642
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?