Ms. Wong is redecorating her office. She has a choice of 7 colors of paint, 4 kinds of curtains, 3 colors of carpet, and 2 styles of furniture. How many different ways are there to redecorate if she chooses two different colors of paint, one kind of curtain, one color of carpet, and one style of furniture?

Question

anonymous · Answer

counting principle for this one
number of ways to pick 2 out of 7 for the paint is written $\dbinom{7}{2}$ read "seven choose two" and computed via $\dbinom{7}{2}=\frac{7\times 6}{2}=7\times 3=21$
multiply 21 by all the other choices for you answer