How many different ways can 4 students be selected from a group of 10?

1 question

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Q: How many different ways can 4 students be selected from a group of 10?

Solution: The number of ways to choose 4 from 10 is given by 10C4 = 210.

Steps: 11

Step 1: Understand that we want to choose 4 students from a total of 10 students.
Step 2: Recognize that this is a combination problem because the order in which we select the students does not matter.
Step 3: Use the combination formula, which is written as nCr, where n is the total number of items (students) and r is the number of items to choose. The formula is nCr = n! / (r! * (n - r)!).
Step 4: In our case, n = 10 and r = 4. So we need to calculate 10C4.
Step 5: Plug the values into the formula: 10C4 = 10! / (4! * (10 - 4)!) = 10! / (4! * 6!).
Step 6: Calculate 10! (10 factorial), which is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, but we can simplify it by canceling out 6! in the denominator.
Step 7: This simplifies to (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1).
Step 8: Calculate the numerator: 10 x 9 x 8 x 7 = 5040.
Step 9: Calculate the denominator: 4 x 3 x 2 x 1 = 24.
Step 10: Divide the numerator by the denominator: 5040 / 24 = 210.
Step 11: Conclude that there are 210 different ways to select 4 students from a group of 10.