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Calculate the following combination

Calculate the following combination-example-1
User Elpidio
by
7.9k points

1 Answer

1 vote

Answer:


_(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

User Jrizzo
by
8.4k points

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