Question

An art gallery has 9 paintings to display along a hallway. How many different ways can they choose and display 6 of the paintings?

Answer 1

There are 84 different ways the art gallery can choose and display 6 paintings out of 9.

Step-by-step explanation:

To find the number of different ways the art gallery can choose and display 6 paintings out of 9, we can use the concept of combinations. A combination is a selection of objects without regard to the order in which they are chosen.

The formula to calculate combinations is given by C(n, r) = n!/((n-r)! * r!), where n is the total number of objects and r is the number of objects to be chosen.

Using this formula for the given problem, we have:

C(9, 6) = 9!/((9-6)! * 6!) = 9!/3! * 6! = (9 * 8 * 7)/(3 * 2 * 1) = 84

Therefore, there are 84 different ways the art gallery can choose and display 6 paintings out of 9.

Answer 2

All you would really need to do is 9*6 = 54 and that's how many different ways you can choose and display the paintings.