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.

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.

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