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A gym teacher needs to choose 15 students out of 20 to participate in a game of dodgeball. How many different teams of fifteen students can be formed without repetition?

Answer :

Final answer:

The number of different teams of fifteen students that can be formed from a group of twenty, without repetition, is calculated using the combination formula from combinatorics. In this case, there are 15504 possible combinations.

Explanation:

To answer this question, we use the concept of combinations in mathematics, specifically from the field of combinatorics. Combinations refer to the selection of items from a larger group where the order of selection does not matter. In this case, we can use the combinations formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of students, k is the number of students being chosen, and ! is the factorial function, meaning the product of all positive integers up to that number.

Applying this formula to your scenario, where the total number of students n is 20 and we want to select k = 15 students, the calculation becomes C(20, 15) = 20! / [15!(20-15)!]. This results in 15504 different teams that can be formed from 20 students without repetition.

Learn more about Combinations here:

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