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QuestionOccupational Safety and Health Administration

Which form is used to record combinations of security containers?
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Step 1
In mathematics, combinations are used to represent the number of ways to choose items from a larger set without regard to the order.

C(10,3)=10!3!(10−3)!=10×9×8×7×6×5×4×3×2×1(3×2×1)(7×6×5×4×3×2×1)=120C(10, 3) = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(3 \times 2 \times 1)(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)} = 120
Combinations are often used in counting problems, including those involving security containers. To record combinations of security containers, we can use the combination formula, which is given by: where: - 1$ containers, without considering the order in which they are chosen. For example, if there are 10 security containers and we want to choose 3 of them, we can use the combination formula to calculate the number of possible combinations: Therefore, there are 120 possible combinations of 3 security containers that can be chosen from a set of 10 containers. In summary, combinations of security containers can be recorded using the combination formula, which provides the number of ways to choose a subset of containers from a larger set without regard to the order in which they are chosen.

Final Answer

C(10,3)=10!3!(10−3)!=10×9×8×7×6×5×4×3×2×1(3×2×1)(7×6×5×4×3×2×1)=120C(10, 3) = \frac{10!}{3!(10 - 3)!} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(3 \times 2 \times 1)(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)} = 120

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