An elementary school art class teacher plans to display artwork next to the door of each...
An elementary school art class teacher plans to display artwork next to the door of each of the classrooms in the school. Each classroom door will only have one piece of artwork displayed, and the school has 35 such doors. If the teacher has 22 oil paintings and 17 sketches, what is the probability that 19 oil paintings and 16 sketches are chosen to be displayed?
Homework Answers
Answer
Total number of oil paintings and sketches = 20+17 = 39 (this is n)
we need only 35 oil paintings and sketches, so r = 35
total number of ways of selecting 35 out of 37 = C(n,r) = C(39,35)
Number of ways of selecting 19 oil paintings out of a total 22 = C(n,r) = C(22,19)
and
Number of ways of selecting 16 sketches out of a total 17 = C(n,r) = C(17,16)
Required probability = favorable outcome/total outcome
= [C(22,19)*C(17,16)]/C(39,35)
= [{22!/((22-19)!*19!}*{17!/((17-16)!*16!}]/{39!/((39-35)!*35!}
= [1540*17]/82251
= 0.3183
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