I took a test in statistics yesterday and I still can't figure this one question out...?

I was doing fine on the test until I got to the last question. It was on probability and permutations, combinations, and multiplication of choices...

The question was something like:

There are persons A, B, C, D, and E sitting at a movie theater in one row. How many ways can they sit in these five seats as long as C is to the right of, but not neccessarily next to B?

I knew how to get the first part of the total number of ways... How do you figure out how many to deduct because of the stipulation involving B and C? Can you take me through the steps. I am so pissed because my mind went blank and I just put the answer to the first part....

I took a test in statistics yesterday and I still can't figure this one question out...?sheet music

I would have just looked at the different possible scenarios

_1_ _2_ _3_ _4_ C (C is definitely to the right of B)

_1_ _2_ _3_ C _3_ (B cannot be chosen on the right of C)

_1_ _2_ C _2_ _3_ (Only A,D,E can be on right)

B C _1_ _2_ _ 3_

24 + 18 + 12 +6 = 60 ways

I took a test in statistics yesterday and I still can't figure this one question out...?state theatre opera theater

if B sits the leftmost, C can sit in any other 4 and still being B's right. other 3 can be arrange as 3P3.

if B 2nd left most, C may have his seat in any 3 of B's right. and so on, putting B first, and making sure C follow the rule(s) and placing the others last.

BC placing

= 4+3+2+1

= 10

ADE placing

= 3P3

= 6

placing all 5

= placing BC * placing ADE

= 10*6

= 60