Question

alicia has 6 paintings she wants to hang side by side on her wall, if she only wants to display 4 of the paintings in how manys can she choose the paintings she wishes to display

Answer 1

6 choice for the left most painting
5 for the 2nd
4 for the 3rd
3 for the last


6*5*4*3

.... but since the order of paintings doesn't matter ... and there are 4! ways to order any four paintings we divide by 4!

Answer 2

\[={6! \over2!}\div4!\]=(6 choose 4)