How many ways to arrange 4 students in a line from a group of 6?

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Question: How many ways to arrange 4 students in a line from a group of 6?

Option a: 24. This would be the number of ways to arrange 4 students if we were choosing and arranging only 2 or perhaps assuming repetition, but for arranging 4 distinct students in a line from 6, 24 is too small. It resembles 4! but ignores the fact that the pool is 6, not 4.

Option b: 120. This matches 5!, or it could arise from 6P4 with a miscalculation. However, 120 is 5!, not the correct product for selecting and ordering 4 students out of 6, since the first position has 6 choices, the second 5, the third 4, and the fourth 3.

Option c: 360. This aligns with the permutation calculation 6P4 = 6 × 5 × 4 × 3. Each of the four positions in the line must be filled by a distinct student from the 6, without repetition, so multiply the available choices at each step.

Option d: 840. This number is larger than 6P4 and could arise from combinations of choosing 4 out of 6 and then permuting, but that would be 6C4 × 4! = 15 × 24 = 360, not 840. It may reflect a misapplied formula or double-counting in some reasoning.

In summary, the problem asks for the number of ordered arrangements (permutations) of 4 students selected from 6, where order matters and no student is repeated. The correct approach is to use permutation counting: 6 × 5 × 4 × 3, which equals 360, matching Option c.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

How many ways to arrange 4 students in a line from a group of 6?

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