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A football team has 99 players. Each pl ayer has a uniform number from 1 to 99 and no two players share the same number. When football practice ends, all the players run off the field one-by-one in a completely random manner. What is the probability that the first four players off the field will leave in order of increasing uniform numbers (e.g., #2, then #6, then #67, then #72, etc)?
  • a)
    1/64
  • b)
    1/48
  • c)
    1/36
  • d)
    1/24
  • e)
    1/16
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A football team has 99 players. Each pl ayer has a uniform number from...
Every player has an equal chance of leaving at any particular time. Thus, the probability that four particular players leave the field first is equal to the probability that any other four players leave the field first. In other words, the answer to this problem is completely independent of which four players leave first.
Given the four players that leave first, there are 4! or 24 orders in which these players can leave the field - only one of which is in increasing order of uniform numbers. (For example, assume the players have the numbers 1, 2, 3, and 4. There are 24 ways to arrange these 4 numbers: 1234, 1243, 1324, 1342, 1423, 1432, . . . , etc. Only one of these arrangements is in increasing order.)
Thus, the probability that the first four players leave the field in increasing order of their uniform numbers is 1/24. 
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Most Upvoted Answer
A football team has 99 players. Each pl ayer has a uniform number from...
Probability Calculation:
- Total number of ways to order the first four players: 99P4 (99 choices for the first player, 98 for the second, and so on)
- Total number of ways for the first four players to leave in increasing order: 1 (only one specific order)
- Probability = 1 / 99P4
- Simplifying the formula: Probability = 1 / (99*98*97*96) = 1/24
Therefore, the probability that the first four players off the field will leave in order of increasing uniform numbers is 1/24, which corresponds to option 'D'.
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A football team has 99 players. Each pl ayer has a uniform number from 1 to 99 and no two players share the same number. When football practice ends, all the players run off the field one-by-one in a completelyrandom manner. What is the probability that the first four players off the field will leave in order of increasing uniform numbers (e.g., #2, then #6, then #67, then #72, etc)?a)1/64b)1/48c)1/36d)1/24e)1/16Correct answer is option 'D'. Can you explain this answer?
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