Question

How many ways can 11 Redcoat basketball players and Coach Woodburn (12 people) be arranged along the sidelines:

a) if Travis and Pat stand together

Answer 1

Already got the answer, just want to confirm it.

Answer 2

I got 79, 833, 600 ways

Answer 3

@jim_thompson5910 @Hero @dan815

Answer 4

If I'm not wrong, there is 22 ways Pat and Travis can stand together 10! ways the remaining 10 people can stand. So the answer should be 22 * 10!. Correct?

Answer 5

Basically, for this, you are supposed to treat Travis and Pat as one unit. So there are really 11 units. Therefore, the number of ways 11 units can be arranged is 11!

Answer 6

NO THOUGH @Hero Notice that if they are 1 single unit they can take the 1st and second position respectively, 2nd and 3rd, and so on till 11th and 12th positions. This is a total of 11 placements. But within these 11 placements, if they were to switch places, for example if travis was on the left pat for these 11 placements, then switch pat with travis would yield another 11 placements for a total of 22. And then to arrange the remaining 10 people there would be 10! factorial ways. So the answer should be 22 x 10!. How did you get just 11!?

Answer 7

22 x 10! is the same as saying 11! x 2.

Answer 8

I'll double check on it.

Answer 9

Just did a google search and found this:

http://ca.answers.yahoo.com/question/index?qid=20101122155237AAhswfl

Turns out that I am correct. @Hero

Answer 10

I see.

Answer 11

Yes, that's exactly correct. It's 2(11!) Great job.