Question

How many ways can Hannah give three of her eight T-shirts to her younger sister?

Answer 1

If Hannah gives her younger sister 3 shirts, it does not matter what order she hands them to her. No matter the order, it will still be the same group of 3 shirt. Since order is not important this problem can be solved using a combination.

Specifically we are asked to find 8C3 (sometimes called "8 choose 3"). This is a fraction. In the numerator we start with 8 and count down 3 numbers. In the denominator we start with 3 and count all the way down to 1. Thus we obtain,

$\frac{(8)(7)(6)}{(3)(2)(1)}=(8)(7)=56$