In how many ways can you select 12 paintings out of a collection of 20 to hang in your art gallery?

[tex]{}_{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]

To determine the number of ways to select 12 paintings out of a collection of 20, we use the concept of combinations. The formula for combinations is given by:

[tex]\[
{}_nC_r = \frac{n!}{r!(n-r)!}
\][/tex]

Where:
- [tex]\( n \)[/tex] is the total number of items to choose from.
- [tex]\( r \)[/tex] is the number of items to choose.
- [tex]\( ! \)[/tex] denotes factorial, meaning the product of all positive integers up to that number.

In this scenario:
- [tex]\( n = 20 \)[/tex] (the total number of paintings),
- [tex]\( r = 12 \)[/tex] (the number of paintings we want to select).

Let's apply the formula:

1. Calculate the factorials:
- [tex]\( 20! \)[/tex] is the factorial of 20.
- [tex]\( 12! \)[/tex] is the factorial of 12.
- [tex]\( (20 - 12)! \)[/tex] is the factorial of 8.

2. Substitute these into the combinations formula:

[tex]\[
{}_{20}C_{12} = \frac{20!}{12! \times 8!}
\][/tex]

3. Calculate the value:

By calculating this using the properties of factorials, we end up with a specific number of combinations.

Therefore, the number of ways to select 12 paintings from 20 is 125,970.

In how many ways can you select 12 paintings out of a collection of 20 to hang in your art gallery?[tex]{}_{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]

Answer :

Other Questions

In how many ways can you select 12 paintings out of a collection of 20 to hang in your art gallery?

[tex]{}_{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]