Question

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. How many ways are there to choose the paintings?

Answer 1

165 ways

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

`^(11)C_3`

Formula for combination is
`^nC_r=(n!)/(r!(n-r)!)`

Using this formula, we have

`^(11)C_3\\\\=(11!)/(3!8!)\\\\=(8!*9*10*11)/(3!8!)\\\\=(9*10*11)/(6)\\\\=165`

Therefore, total number of ways = 165

Answer 2

165 ways to choose the paintings

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.