How do you evaluate {}^2C_2?
How do you evaluate {}^2C_2?
Aniket Singh , 1 Year ago
Grade
11 grade maths others> How do you evaluate {}^2C_2?...
1 AnswersAskiitians Tutor Team
To evaluate \({}^2{C_2}\), we use the formula for combinations:
\[
{}^n{C_r} = \frac{n!}{r!(n - r)!}
\]
In this case, \(n = 2\) and \(r = 2\), so we substitute these values into the formula:
\[
{}^2{C_2} = \frac{2!}{2!(2 - 2)!}
\]
Now, calculate the factorials:
- \(2! = 2 \times 1 = 2\)
- \((2 - 2)! = 0! = 1\) (by definition, \(0! = 1\))
Substitute these values back into the equation:
\[
{}^2{C_2} = \frac{2}{2 \times 1} = \frac{2}{2} = 1
\]
Therefore, the value of \({}^2{C_2}\) is 1.
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