Suppose that 10 people, including you and a friend, line up for a group picture. how many ways can the photographer rearrange the line if she wants to keep exactly three people between you and your friend?

483 840 ways

Step-by-step explanation:

Let you and your friend be A and B.

With three people always between you two,, we have

Case 1: AxxxB

Case 2: xAxxxB

Case 3: xxAxxxBxxx

Case 4: xxxAxxxBxx

Case 5: AxxxBx

Case 6: AxxxB

So there is 6 ways of arranging you two through the line and for each of the six cases,

If you two remained in your positions, the rest can be arranged in 8! ways

Also for each case, you two can interchange your positions in 2! ways

Therefore,

The photographer can rearranged the line keep three people between you an your friend in

8! * 2! * 6 = 483 840 ways

answer:

step-by-step explanation:

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.