How many ways can you choose 3 students from a group of 10?

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Question: How many ways can you choose 3 students from a group of 10?

Options:

Correct Answer: 210

Solution:

The number of combinations is calculated as 10C3 = 10! / (3!(10-3)!) = 120.

How many ways can you choose 3 students from a group of 10?

How many ways can you choose 3 students from a group of 10?

Step 1: Understand that we want to choose 3 students from a group of 10.
Step 2: Recognize that the order in which we choose the students does not matter, so we will use combinations.
Step 3: The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 4: In our case, n = 10 (total students) and r = 3 (students to choose).
Step 5: Plug the values into the formula: 10C3 = 10! / (3!(10-3)!)
Step 6: Simplify the formula: 10C3 = 10! / (3! * 7!)
Step 7: Calculate 10! (10 factorial) which is 10 x 9 x 8 x 7! (we can cancel 7! in the numerator and denominator).
Step 8: Now we have: 10C3 = (10 x 9 x 8) / (3 x 2 x 1).
Step 9: Calculate the numerator: 10 x 9 x 8 = 720.
Step 10: Calculate the denominator: 3 x 2 x 1 = 6.
Step 11: Divide the numerator by the denominator: 720 / 6 = 120.
Step 12: Therefore, there are 120 ways to choose 3 students from a group of 10.

Combinations – The concept of combinations involves selecting items from a larger set where the order of selection does not matter.
Factorial – Factorial is a mathematical operation that multiplies a number by all positive integers less than it, denoted by n!.