Answer: a) 720
b) 144
c) 480
Step-by-step explanation:
a) 6 people changing places in a line is permutation (because the a line has a order)
This way, 6 people in a line is 6! = 6.5.4.3.2.1 = 720
b) We can consider 4 people a block that will permut, so, instead of 6 people we have 3 [a block of 4 people and 2 more):
3! = 3.2.1 = 6
This group of 4 can also permut, so 4! = 4.3.2.1 = 24
Total = 3!.4! = 6.24=144
c) For this case, the easiest way is doing the complement. Calculate how many the 2 people are together and subtract from the total, so:
We can consider 2 people a block that will permut, so, instead of 6 people we have 5 [a block of 2 people and 4 more):
5! = 5.4.3.2.1 = 120
The 2 people from the block will permut as well:
2! = 2.1 = 2
Total: 5!.2! = 120.2 = 240.
For the case they are not following each other:
720 - 240 = 480
