# College Finite

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Assume that the student
has a cup with 13 writing implements: 7 pencils, 4 ball
point pens, and 2 felt-tip pens.
In how many ways can the selection be made if no more than one ball
point pen is selected?

• College Finite -

The question is not clear.
Must he choose one of each?
Could he just take 1 pencil?

I will assume anything goes, except must be 0 ballpoint or 1 ball point

two ways to pick the ball points, either pick none or one
8 ways to pick the pencil, either pick none, or pick one, or pick 2 .... or pick 7
3 ways to pick the felt-tips, either pick one, or pick one , or pick 2

number of possible selections = 2x8x5 = 80

but that would include the 1 case of picking no pencil, picking no ballpoint and picking no felt-tip

so final number of ways = 80-1 = 79

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