Assume that the student
has a cup with 15 writing implements: 8 pencils, 5 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?
"In how many ways can the selection be made if no more than one ball point pen is selected?"
your question is not clear.
Are the pencils all the same ? etc
Is one ball-point, 6 pencils and 2 felt-tips a "selection" ?
Is just one pencil a "selection" ?
You have to define what you mean by a selection.
I don't know the answer but i know the answer is not 53. Not all info was givin to complete the problem. It should have read that they student will select 5 writing implements. How many ways if only one ball poin at selected.
To determine the number of ways the selection can be made, we'll consider the different cases separately:
Case 1: No ballpoint pen is selected.
In this case, we can select any combination of pencils and felt-tip pens. Since we have 8 pencils and 2 felt-tip pens, the number of ways to select them would be the sum of the following possibilities:
- Selecting 0 pencils and 2 felt-tip pens: 1 way
- Selecting 1 pencil and 1 felt-tip pen: 2 ways
- Selecting 2 pencils and 0 felt-tip pens: 1 way
So the total number of ways in this case is 1 + 2 + 1 = 4.
Case 2: One ballpoint pen is selected.
In this case, we can select 1 ballpoint pen and any combination of pencils and felt-tip pens. Since we have 5 ballpoint pens, the number of ways to select one of them would be 5. The remaining selection can be done using the same logic as in Case 1, with 7 pencils and 2 felt-tip pens.
So the total number of ways in this case is 5 × 4 = 20.
Therefore, the total number of ways to make the selection without selecting more than one ballpoint pen is 4 + 20 = 24 ways.
I thought it over and I would do it this way:
the pencils can be taken in 9 ways, that is,
take none, 1,2,3,.. or 8 of them
the ball-point pens can be taken in 2 ways, none or 1
the felt-tips in 3 ways, none, one or both.
number of selections = 9(2)(3) or 54
But that would include the case of taking none at all, which would not be a selection,
so number of selections is 54-1 or
53 ways.