A math professor wears for each class a combination of : one of their three hats (red, blue, green); one of their pants (black, blue, white, green); one of their shirts (white, red, black);and one of their pair of shoes (black, red, blue, white). They never wear combinations withthree items of the same color. How many different combinations are wearable?

There are 36 ways in which he can wear combinations with three items of the different color.

Step-by-step explanation:

Hat              Pants           Shirts           Shoes

red             black             red              black

blue           blue               black           red

green        green             white            blue

                 white                                  white

If we look carefully we see that he can choose any hat, any pant and any shirt but he can choose only one pair of shoes that does not match with any of the three.

3C1*4C1*3C1*4C4= 3*4*3* 1= 36

There are 36 ways in which he can wear combinations with three items of the different color.

the answer is 13 cm