Hello everyone

I don't see any particular ambiguity in the way the question is phrased. I have assumed that it means:

How many ways are there of choosing and arranging $\displaystyle \displaystyle r$ items from a set of $\displaystyle \displaystyle n$, if a certain group of $\displaystyle \displaystyle p$ items must always be included in the arrangement?

The question Plato has answered is quite different. He has interpreted it as:

How many ways are there of arranging $\displaystyle \displaystyle n$ items, if a certain group of $\displaystyle \displaystyle p$ items *must be placed together in a block* within the arrangement?

There doesn't seem any room for the variable $\displaystyle \displaystyle r$ within this latter interpretation.

Grandad