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$12C2$

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Combinations and permutations

Full solution

Q.

12C2

Use Combination Formula: To solve $12C2$ , we use the combination formula: $nCr = \frac{n!}{(r!(n-r)!)}$
Calculate Factorial of $12$ : First, calculate the factorial of $12$ , which is $12! = 12 \times 11 \times 10 \times \ldots \times 1$
Calculate Factorial of $2$ : Then, calculate the factorial of $2$ , which is $2! = 2 \times 1$
Calculate Factorial of $(12-2)$ : Also, calculate the factorial of $(12-2)$ , which is $10! = 10 \times 9 \times \ldots \times 1$
Plug into Formula: Now plug these into the formula: $12C2 = \frac{12!}{(2! \times (12-2)!)}$
Simplify Factorials: Simplify the factorials in the formula: $12C2 = \frac{12 \times 11 \times 10!}{2 \times 1 \times 10!}$
Cancel Common Factorial: Cancel out the common $10!$ from numerator and denominator: $12C2 = \frac{12 \times 11}{2 \times 1}$
Perform Division and Multiplication: Perform the division and multiplication: $12C2 = \frac{12 \times 11}{2} = \frac{132}{2}$
Final Answer: Finally, divide $132$ by $2$ to get the answer: $12C2 = 66$

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