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Eleven football players form a huddle on the field so the quarterback can announce the next play. How many different ways can the players be arranged to form thisnhuddle

User Tambre
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Final answer:

There are 3,628,800 different ways eleven football players can be arranged to form a huddle, calculated using the formula for circular permutations (n - 1)! where n is the number of players.

Step-by-step explanation:

To determine how many different ways eleven football players can be arranged to form a huddle, we must consider the mathematical concept of permutations, as each player's position matters, and a huddle is a circular arrangement. In a circular permutation, we remove the fixation of position which we usually have in linear permutations. If there are n distinct items to be arranged in a circle, there are (n - 1)! different arrangements. Since the huddle consists of eleven players, we use the formula for circular permutations to determine the number of different ways they can form a huddle:

  • Number of ways = (n - 1)! = (11 - 1)! = 10!
  • 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

Therefore, there are 3,628,800 different ways the eleven football players can be arranged in the huddle.

User Aaron Greenwald
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