Question 618086: I am stuck on this question:
If a student must take six tests:
T1, T2, T3, T4, T5, T6.
In how many ways can the student take the tests if:
a.) T2 must be taken immediately after T1?
b.) T1 and T2 cannot be taken immediately after one another?
I first tried coming up with all of the options for T1 followed by T2, but it will take forever!!:
1,2,3,4,5,6
1,2,3,4,6,5
1,2,3,6,4,5
1,2,3,6,5,4
1,2,3,5,6,4
1,2,3,5,4,6
1,2,4,3,5,6
1,2,4,3,6,5
1,2,4,5,3,6
1,2,4,5,6,3
1,2,4,6,3,5
1,2,4,6,5,3
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! a.) treat T1/T2 as a single entity, so you are working with 5 tests instead of 6
___ should be 5!
b.) similar argument
___ now two entities, T1/T2 and T2/T1
___ so 2 * 5! not allowed
___ 6! - (2 * 5!)
6! is the number of ways of arranging 6 things in order
___ when T1 and and T2 become a single thing, then there are 5 things to arrange in order; so 5!
___ in b, there are two arrangements of T1 and T2; so 5! is subtracted twice from the total possible arrangements
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