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Five students, Leah, Fawzia, Yusuf, Hailey, and Autumn, line up one behind the other. How many different ways can they stand in line? Answer:

Five students, Leah, Fawzia, Yusuf, Hailey, and Autumn, line up one behind the other. How many different ways can they stand in line?\newlineAnswer:

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Full solution

Q. Five students, Leah, Fawzia, Yusuf, Hailey, and Autumn, line up one behind the other. How many different ways can they stand in line?\newlineAnswer:
  1. Identify Problem: Identify the problem.\newlineWe need to find the number of different arrangements for 55 students standing in line. This is a permutation problem where order matters.
  2. Determine Formula: Determine the formula to use.\newlineThe number of ways to arrange nn distinct objects in a sequence is given by nn factorial, denoted as n!n!.
  3. Apply Formula: Apply the formula to the given problem.\newlineSince there are 55 students, we need to calculate 5!5! (55 factorial).\newline5!=5×4×3×2×15! = 5 \times 4 \times 3 \times 2 \times 1
  4. Perform Calculation: Perform the calculation. 5!=5×4×3×2×1=1205! = 5 \times 4 \times 3 \times 2 \times 1 = 120
  5. Conclude Answer: Conclude with the final answer.\newlineThere are 120120 different ways the five students can stand in line.

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