There are 10 people on a basketball team, and the coach needs to choose 5 to put into a game. How many different possible ways can the coach choose a team of 5 if each person has an equal chance of being selected? Answer:

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Calculate Combinations Formula: To solve this problem, we need to calculate the number of combinations of 10 people taken 5 at a time. The formula for combinations is given by: C(n, k) = n! / (k! * (n - k)!) where n is the total number of items, k is the number of items to choose, and ! denotes factorial. In this case, n = 10 and k = 5.Calculate Factorial of n: First, we calculate the factorial of n, which is 10!. 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1Calculate Factorial of k: Next, we calculate the factorial of k, which is 5!. 5! = 5 * 4 * 3 * 2 * 1Calculate Factorial of n - k: We also need to calculate the factorial of n - k, which is 10 - 5 = 5, so we need 5! again. Since we've already calculated 5!, we can use the same value.Plug Values into Formula: Now we can plug these values into the combinations formula: C(10, 5) = 10! / (5! * (10 - 5)!) C(10, 5) = 10! / (5! * 5!)Substitute Factorial Values: Substitute the factorial values we've calculated into the formula: C(10, 5) = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((5 * 4 * 3 * 2 * 1) * (5 * 4 * 3 * 2 * 1))Simplify Expression: We can simplify the expression by canceling out the common factors in the numerator and the denominator: C(10, 5) = (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)Further Simplification: Further simplification gives us: C(10, 5) = (10/5) * (9/1) * (8/4) * (7/1) * (6/2) C(10, 5) = 2 * 9 * 2 * 7 * 3Multiply to Get Result: Multiplying these together, we get: C(10, 5) = 2 * 9 * 2 * 7 * 3 C(10, 5) = 18 * 14 * 3 C(10, 5) = 252 * 3 C(10, 5) = 756

There are $10$ people on a basketball team, and the coach needs to choose $5$ to put into a game. How many different possible ways can the coach choose a team of $5$ if each person has an equal chance of being selected? $\newline$ Answer:

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There are $10$ people on a basketball team, and the coach needs to choose $5$ to put into a game. How many different possible ways can the coach choose a team of $5$ if each person has an equal chance of being selected? $\newline$ Answer: