Counting principles, three letter sequence w/o repeated letters, containing e or f
How many three-letter sequences without repeated letters can be made using a,b,c,d,e,f in which either e or f (or both) is used?
I looked at the total sequences posible with all letters:
6*5*4=120 this is w/o replacement
The I looked at the amount of sequences without e or f:
Then I substract the amount of sequences without e or f from the total amount of possible sequences:
(6*5*4)-(4*3*2)=96 amount of sequences with e or f
But now I want to find the amount of sequences with e or f directly.
Here I have a problem because it is e or f.
If I would look for "without repetition and containing the letter g," I would do
g _ _ 5 * 4 = 20
NOg g _ 5 * 4 = 20
NOg NOg g 5 * 4 = 20 and then add it up 20 + 20 + 20 = 60
How can I do this with g or f?