In how many ways can the student select 7 writing implements? In how many ways can the selection be made if no more than one ball point pen is selected?

Question

Assume that the student has a cup with 13 writing implements: 6 pencils, 5 ball point pens, and 2 felt-tip pens.

Answer 1

Answer to first question: 13 choose 7 = 1716

Answer to second question: 2 cases: 1) 1 ball point pen is selected 2) no ball point pen is selected

1) (5 choose 1)(8 choose 6) = 140

2) (8 choose 7) = 8

so 148