Story problem

[ptonsparky]

I have a bulk storage that includes 11 tanks. Materials can and are moved from any of the tanks to any of the others, plus two destinations for shipping. There is also one source for receiving product (A).

Fifteen different motors are used to move the product as needed. I need to decide which motors must start for each combination of Source & Destination.

Tanks 1-10 can be a source for product, plus A. Total of 11 sources.
Tanks 1-10 can be a destination for product, plus C & D. Total of 12 destinations.
"A" can not be a destination. C or D can not be a source. The source cannot equal the destination. (I do not want to take product from 1 and dump it back into 1.)

How many different combinations of Source Destination are possible?

I have managed 119.

 

[steve66]

Source A has 12 destinations. Thats 1 X 12.

Then you have 10 sources each with 11 destinations. (eleven and not twelve because we subtract one since the same source cant be the destination.) That's 10 X 11 = 110.

So I get 12 + 110 = 122 combinations.

Can anyone confirm or figure out if I went wrong somewhere?
Steve

 

[mivey]

I agree with 122 per Steve66's analysis.

[edit: although I don't get why if tank#11 can't be another source or destination since the OP said product can move between any two tanks. That would give another 20 combinations (10 more for Tank#11 to tanks #1-10 plus 10 more for tanks #1-10 to tank #11]