STATISTICS - COMBINATION?

PROBLEM A:

You have 4 colors and you are picking 1 to paint *all* the benches.

C(4,1) = 4 ways

Answer:

4

PROBLEM B:

You have four options:

1) 3 benches in one color, 1 bench in another color.

You have 4 color choices for the three benches and 3 color choices for the single bench

= 4 x 3

= 12

2) 2 benches in one color, 2 benches in another color.

You have 4 colors and you are picking 2 of them. The order of the color doesn't matter because you have the same number of benches in each color.

C(4,2) = 4 x 3 / 2

= 6

3) 2 benches in one color, 1 bench in another, 1 bench in another.

You have 4 colors for the pair of benches. Then from the remaining 3 colors, pick 2 for the single benches.

4 * C(3,2)

= 4 * 3

= 12

4) 4 benches of all different colors.

There's only one way to paint all 4 benches in 4 different colors

= 1

Answer:

12 + 6 + 12 + 1

= 31 ways

PROBLEM C:

Only 1 way (see #4 above)

PROBLEM D:

First he paints to benches red so he only has to worry about the remaining benches.

You have two options:

Remaining two benches are the same color --> C(4,1) = 4 ways

Remaining two benches are two different colors --> C(4,2) = 6 ways

Answer:

4 + 6

= 10 ways

There are a million different ways he can paint the benches.

I can't list them all here, sorry.