SOLUTION: Assume that the student has a cup with 10 writing implements: 5 pencils, 3 ball point pens, and 2 felt-tip pens. (1) In how many ways can the student select 4 writing implements

Question 1199915: Assume that the student has a cup with 10 writing implements: 5 pencils, 3 ball point pens, and 2 felt-tip pens.
(1) In how many ways can the student select 4 writing implements?
(2) In how many ways can the selection be made if no more than one ball point pen is selected?

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

(1) choose 4 implements out of 10 total: C(10,4) = 210

(2) choose 1 ball point pen and 3 of the other 7 implements, or 0 ball point pens and 4 of the other 7: C(3,1)*C(7,3) + C(3,0)*C(7,4) = 3*35 + 1*35 = 140

You can get good practice performing this kind of calculations by finding the number of ways of getting 2 or 3 ball point pens and verifying that the total number of ways of choosing 4 of the implements, using any number of ball point pens, is equal to the total number of ways, 210:

2 ball point pens and 2 of the other 7: C(3,2)*C(7,2) = 3*21 = 63
3 ball point pens and 1 of the other 7: C(3,3)*C(7,1) = 1*7 = 7

140+63+7 = 210

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