In how many ways can 6 different flags be arranged on a pole?

In how many ways can 6 different flags be arranged on a pole?

Step 1: Understand that we have 6 different flags to arrange.
Step 2: Recognize that arranging these flags is a permutation problem, where the order matters.
Step 3: Recall the formula for permutations of n different items, which is n! (n factorial).
Step 4: Since we have 6 flags, we need to calculate 6!. This means we multiply 6 by every whole number less than it down to 1.
Step 5: Calculate 6! = 6 × 5 × 4 × 3 × 2 × 1.
Step 6: Perform the multiplication: 6 × 5 = 30, then 30 × 4 = 120, then 120 × 3 = 360, then 360 × 2 = 720, and finally 720 × 1 = 720.
Step 7: Conclude that there are 720 different ways to arrange the 6 flags on the pole.

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