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Antimeio

Answered question

2022-12-13

How do you evaluate

^{10} C_{3}

natach0uille3us

Beginner2022-12-14Added 1 answers

Evaluating the expression

^{10} C_{3}

:
As we know, a combination is a grouping or subset of items.
We will evaluate the given expression

^{10} C_{3}

by using the combination formula.
The order does not matter in a combination.
So,

\Rightarrow C^{(n, r)} =^{n} C_{r}

\Rightarrow

C r n = \frac{n!}{(n - r)! r!}

Here,

n

is the number of items in the set and

r

is the number of items selected from the set.

\Rightarrow

C 3 10 = \frac{10!}{(10 - 3)! \times (3!)}

\Rightarrow

\frac{10 \times 9 \times 8 \times 7 \times 6 \times . . . \times 1}{7 \times 6 \times . . . \times 1 \cdot (3 \times 2 \times 1)}

\Rightarrow

\frac{10 \times 9 \times 8}{3 \times 2 \times 1}

\Rightarrow^{10} C_{3} = 120

Hence, the value of

^{10} C_{3}

120

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