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Data Interview Question

Arranging Three Contestants

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Solution & Explanation

When arranging three contestants in a podium with three positions (1st, 2nd, and 3rd), the problem is essentially about finding the number of permutations of three distinct objects. Permutations are arrangements where the order of the items matters.

Step-by-step Explanation:

  1. Understanding the Problem:

    • We have three participants, let's label them as A, B, and C.
    • We need to determine how many different ways they can be arranged in the three positions available.

  2. Using the Permutation Formula:

    • The formula for permutations of n distinct objects is given by n! (n factorial), which is the product of all positive integers up to n.
    • In this case, n = 3, so we calculate 3!.

  3. Calculating Factorial:

    • 3! = 3 × 2 × 1 = 6
    • This calculation shows that there are 6 different ways to arrange the three participants.

  4. Illustrating with an Example:

    • Let's list all possible arrangements to verify our calculation:
      1. A, B, C
      2. A, C, B
      3. B, A, C
      4. B, C, A
      5. C, A, B
      6. C, B, A
    • As you can see, there are indeed 6 unique arrangements.

  5. Breaking Down the Choices:

    • 1st Position:
      • We have 3 options (A, B, C) to fill the 1st position.
    • 2nd Position:
      • After filling the 1st position, only 2 options remain for the 2nd position.
    • 3rd Position:
      • Finally, with the 1st and 2nd positions filled, there is only 1 option left for the 3rd position.
    • Therefore, the total number of arrangements is calculated as:
      • 3 choices (1st) × 2 choices (2nd) × 1 choice (3rd) = 6 arrangements

  6. Conclusion:

    • The total number of possible arrangements for three contestants in three podium positions is 6. This is a straightforward application of the permutation concept, where the order of arrangement is crucial.

By understanding the factorial concept and applying it to the permutation problem, we can confidently determine the number of possible arrangements for the contestants in this scenario.