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.

d

step-by-step explanation:

the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle   we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.