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 student select 9 writing implements if no more than one ball
point pen is selected?
1bp, 2felt, 6pencils
1bp, 1 felt,7 pencils
0bp, 2felt, 7 pencils
can you think of any others?
it has to do with choosing, and combinations/permutations though.
To find the number of ways the student can select 9 writing implements, we can consider different scenarios based on the number of ballpoint pens selected.
1. If no ballpoint pen is selected:
In this case, the student needs to select 9 writing implements from the remaining 11 (7 pencils and 2 felt-tip pens). We can use the combination formula to calculate the number of ways, which is denoted as C(n, r), where n is the total number of items and r is the number of items to be selected. Therefore, the number of ways to select 9 writing implements without any ballpoint pen is C(11, 9) = 55.
2. If exactly one ballpoint pen is selected:
In this case, the student needs to select 8 more writing implements from the remaining 12 (7 pencils, 3 ballpoint pens excluding the one already selected, and 2 felt-tip pens). Again, we can use the combination formula to calculate the number of ways, which is C(12, 8) = 495.
Thus, the total number of ways the student can select 9 writing implements, while no more than one ballpoint pen is selected, is the sum of the two scenarios mentioned above: 55 + 495 = 550.
So, the student can select 9 writing implements in 550 different ways.