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What is the value of the expression 12 c 5 ?
1) 120
2) 792
3) 95040
4) 33264

1 Answer

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Final answer:

The expression 12C5 refers to the number of combinations of 5 items from a set of 12, which is calculated using the formula 12!/(5!*(12-5)!). Simplifying this, the value is determined to be 792, which means the correct answer is option 2.

Step-by-step explanation:

The expression 12 c 5 likely refers to 12 choose 5, which is a combination calculation and can be denoted as 12C5 or nr(n-r)!. This represents the number of ways to choose 5 items from a set of 12 without regard to the order. To calculate it, use the formula:


12C5 = 12! / (5! * (12 - 5)!) = 12! / (5! * 7!)


Calculating the factorial values and simplifying:


12! = 12 × 11 × ... × 1


5! = 5 × 4 × ... × 1


7! = 7 × 6 × ... × 1


This simplifies to:


12C5 = 12 × 11 × 10 × 9 × 8 / (5 × 4 × 3 × 2 × 1)


After canceling out the common factors, the result is:


12C5 = 792


Therefore, the value of the expression 12C5 is 792, which corresponds to option 2.

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