Question

A club has 7 members. threee are to be chosen to go as a group how many distinct groups of 3

Answer 1

There are 7 ways to fill the first slot
6 ways to fill the second slot
5 ways to fill the third and last slot

7*6*5 = 42*5 = 210 different ways to have a 3 person group if order mattered

However, order doesn't matter. A group like {A,B,C} is the same as a group like {B, A, C}. There are 3! = 3*2*1 = 6 ways to order any particular group. So we divide the result of 210 over 6 to get 210/6 = 35

Final Answer: 35

Note: we can get the same answer using the nCr combination formula. Use n = 7 and r = 3