SOLUTION: a club consist of ten members. in how many different ways can a group of three people be selected to go on a trip?

Sometimes that's written

, sometimes  and sometimes 

Sometimes it's called "Ten choose three" and sometimes 
it's called "The number of combinations of ten things 
taken three at a time".

But it always means to make a fraction which has 3 factors in the
numerator and three factors in the denominator  

The three factors in the numerator start with 10 and we subtract 
1 each time until we have three factors.  That is, 10*9*8.

The three factors in the denominator start with 3 and we subtract 
1 each time until we have three factors.  That is, 3*2*1

So the answer is 



This fraction will always reduce to a whole number.

Divide the 3 into the 9 and the 2 into the 8 and you end up with

 or 120 ways to choose a group of 3 out of a group of 10.

Edwin