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 7 writing implements: 4 pencils, 2 ball point pens, and 1 felt-tip pen.

The student draws 4 writing implements. How many ways can the selection be made if no more than one ball point pen is selected?

Answer 1

First, we calculate the number of implements N₀ when no ball pens are selected. Thus we select 4 items from 5 items (4 pencils and 1 felt-tip pen). Therefore, N₀ = 5!/4! = 5.

Second, we calculate the number of implements N₁ when one of two ball pens is selected. In this case we select 3 items from 5 items (4 pencils and 1 felt-tip pen) 5!/3! = 20. N₁ = 2*20 = 40 because there are 2 ball pens.

Total number of the implements is N₀ + N₁ = 45.