Question

Calculate the following combination

Answer 1

`_(3)C_(2)` = 3;
`_(3)C_(3)` = 1

Explanation:

You can start by substituting the values of n and r into the basic formula:

`_(n)C_(r)` =
`(n!)/((n - r)!r!)`

`_(3)C_(2)` =
`(3!)/((3 - 2)! * 2!)`

Now, simplify the numerator and the denominator:

`(3!)/((3 - 2)! * 2!)` =
`(6)/(1 * 2)` = 3

`_(3)C_(2)` = 3

For the second instance, do the same thing:

`_(n)C_(r)` =
`(n!)/((n - r)!r!)`

`_(3)C_(3)` =
`(3!)/((3-3)!*3!)`

Finally, simplify the numerator and denominator:

`(3!)/((3-3)!*3!)` =
`(6)/(6)` = 1

`_(3)C_(3)` = 1