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?
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
To find the number of ways to make the selection, we need to consider two cases:
1. When no ballpoint pen is selected.
2. When exactly one ballpoint pen is selected.
Case 1: No ballpoint pen is selected
In this case, we have to select from 7 pencils and 2 felt-tip pens. Since there are no restrictions, we can use the concept of multiplication to calculate the number of ways.
Number of ways = number of choices for pencils x number of choices for felt-tip pens
Number of ways = 7 pencils x 2 felt-tip pens
Number of ways = 14
Case 2: Exactly one ballpoint pen is selected
In this case, we have to choose one ballpoint pen and select from the remaining 7 pencils and 2 felt-tip pens. Again, we can use the concept of multiplication to calculate the number of ways.
Number of ways = number of choices for ballpoint pen x number of choices for pencils x number of choices for felt-tip pens
Number of ways = 4 ballpoint pens x 7 pencils x 2 felt-tip pens
Number of ways = 56
Now, to get the total number of ways, we can add the number of ways from both cases.
Total number of ways = Number of ways (Case 1) + Number of ways (Case 2)
Total number of ways = 14 + 56
Total number of ways = 70
Therefore, there are 70 ways to make the selection if no more than one ballpoint pen is selected.