Respuesta :
Answer:
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: AxxxBxxxxx
Case 2: xAxxxBxxxx
Case 3: xxAxxxBxxx
Case 4: xxxAxxxBxx
Case 5: xxxxAxxxBx
Case 6: xxxxxAxxxB
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
The question is an illustration of permutation and combination
There are 672 ways to rearrange the 10 people
The total number of people is given as:
[tex]n=10[/tex]
When three people are kept between you and your friend, there are 7 people left, and the three people would be categorized as 1. i.e. 7 + 1 = 8
- There are 8C3 ways to select 3 people from the 8
- There are 3! ways to arrange the 3 people between you and your friend
- There are 2! ways to arrange you and your friend
So, the total number of ways of arrangement is:
[tex]Total = ^8C_3 \times 3! \times 2![/tex]
Evaluate 8C3
[tex]Total = \frac{8!}{(8-3)!3!} \times 3! \times 2![/tex]
This gives
[tex]Total = \frac{8!}{5!3!} \times 3! \times 2![/tex]
Expand the factorials
[tex]Total = \frac{8 \times 7 \times 6 \times 5!}{5!3!} \times 3! \times 2![/tex]
[tex]Total = \frac{8 \times 7 \times 6}{3!} \times 3! \times 2![/tex]
Cancel out common factors
[tex]Total = 8 \times 7 \times 6 \times 2![/tex]
[tex]Total = 672[/tex]
Hence, there are 672 ways to rearrange the 10 people
Read more about permutation and combination at:
https://brainly.com/question/11732255
