Assume that the student
has a cup with 9 writing implements: 4 pencils, 3 ball
point pens, and 2 felt-tip pens.
Students will select 5 writing implements.
In how many ways can the selection be made if no more than one ball
point pen is selected?
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To find out the number of ways the selection can be made, we need to consider different cases where either no ballpoint pen is selected or only one ballpoint pen is selected.
Case 1: No ballpoint pen is selected.
In this case, we have to select 5 writing implements from the remaining 9 (4 pencils and 2 felt-tip pens). Since order doesn't matter, we can use combinations to calculate the number of ways to select the writing implements without a ballpoint pen. The equation for combinations is given by nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items to be selected. In this case, n = 6 (4 pencils + 2 felt-tip pens) and r = 5.
The number of ways to select the writing implements without a ballpoint pen can be calculated as 6C5 = 6! / 5!(6-5)! = 6.
Case 2: Only one ballpoint pen is selected.
In this case, we need to select 1 ballpoint pen and 4 more writing implements from the remaining 8 (3 ballpoint pens, 4 pencils, and 2 felt-tip pens). Again, using combinations, we can calculate the number of ways to select the writing implements with one ballpoint pen. The equation for combinations is nCr = n! / r!(n-r)!, where n = 8 (3 ballpoint pens + 4 pencils + 2 felt-tip pens) and r = 4.
The number of ways to select the writing implements with one ballpoint pen can be calculated as 8C4 = 8! / 4!(8-4)! = 70.
Finally, to find the total number of ways the selection can be made, we add the number of ways from both cases:
Total number of ways = Number of ways without a ballpoint pen + Number of ways with one ballpoint pen = 6 + 70 = 76.
Therefore, there are 76 ways to select 5 writing implements from the cup if no more than one ballpoint pen is selected.