Question

What are the number of ways of selecting 7 files out of 14 distinct files?

Answer 1

Since one file is always selected, we can say that we select that particular file in 1C1 ways.

Now, the number of files that remain is 13 and we need to select 6 files from it as one is already selected. This can be done in 13C6 ways.

To get the number in which we always select a particular file and then select 6 more from the remaining, simultaneously, is given by multiplying the two quantities derived above i.e. 1C1 x 13C6

Hence, the answer to your question is:

1C1 x 13C6 = 1 x 1716 = 1716 ways.