There are 11 paintings at an art show. Three of them are chosen randomly to display in the gallery window. The order in which they are chosen does not matter. H
Question
2 Answer

1. User Answers Hulkk
Answer:
165 ways to choose the paintings
Stepbystep explanation:
This is clearly a Combination problem since we are selecting a few items from a group of items and the order in which we chosen the items does not matter.
The number of possible ways to choose the paintings is;
11C3 = C(11,3) = 165
C denotes the combination function. The above can be read as 11 choose 3 . The above can simply be evaluated using any modern calculator.

2. User Answers SociometricStar
Answer:
165 ways
Stepbystep explanation:
Total number of painting, n = 11
Now, three of them are chosen randomly to display in the gallery window.
Hence, r = 3
Since, order doesn't matter, hence we apply the combination.
Therefore, number of ways in which 3 paintings are chosen from 11 paintings is given by
[tex]^{11}C_3[/tex]
Formula for combination is [tex]^nC_r=\frac{n!}{r!(nr)!}[/tex]
Using this formula, we have
[tex]^{11}C_3\\\\=\frac{11!}{3!8!}\\\\=\frac{8!\times9\times10\times11}{3!8!}\\\\=\frac{9\times10\times11}{6}\\\\=165[/tex]
Therefore, total number of ways = 165