15.
a. using the formula for combinations, show that the number of ways of selecting 2 items from a group of 3 items is the same as the number of ways to select 1 item from a group of 3.
b. show that and − are equal. explain why this makes sense.

Explanation:

a)

b) First, we have that

On the other hand,

Therefore, both expressions are equal. This makes sense, because selecting k elements from a group of n is the same than specify which elements you will not select. In order to specify those elements you need to select the n-k elements that will not be selected. Hence, each time you are selecting k from n, you are also selecting n-k from n, and from that reason both combinatorial numbers are equal.

answer: y = -12x + 108

step-by-step explanation: do (y = m x+b) formula.