Question

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?

Answer 1

Answer: 0.3183

Step-by-step explanation:

Given : Total number of classroom doors =35

Number of oil paintings = 22

Number of sketches = 17

Total artworks = 22+17=39

Total ways of selecting 35 artworks from 39 will be :-

$^{39}C_{35}=\dfrac{39!}{(39-35)!35!}=82251$

Total ways of selecting 19 oil paintings and 16 sketches will be :-

$^{22}C_{19}\times^{17}C_{16}\\\\=\dfrac{22!}{19!3!}\times\dfrac{17!}{16!}=26180$

Now, the probability that 19 oil paintings and 16 sketches are chosen to be displayed is given by :-

$\dfrac{26180}{82251}=0.318294002505\approx0.3183$

Hence, the  probability that 19 oil paintings and 16 sketches are chosen to be displayed =0.3183