How many ways can you select 2 students from a class of 8?

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Question: How many ways can you select 2 students from a class of 8?

Options:

Correct Answer: 28

Solution:

The number of combinations of 8 students taken 2 at a time is C(8, 2) = 8! / (2!(8-2)!) = 28.

How many ways can you select 2 students from a class of 8?

How many ways can you select 2 students from a class of 8?

Step 1: Understand that we want to select 2 students from a total of 8 students.
Step 2: Recognize that the order in which we select the students does not matter. This means we will use combinations, not permutations.
Step 3: Use the combination formula C(n, r) = n! / (r!(n - r)!), where n is the total number of students (8) and r is the number of students to select (2).
Step 4: Plug in the values into the formula: C(8, 2) = 8! / (2!(8 - 2)!).
Step 5: Calculate (8 - 2) which equals 6, so we have C(8, 2) = 8! / (2! * 6!).
Step 6: Calculate 8! (which is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) but notice that 6! will cancel out in the calculation.
Step 7: Simplify the equation: C(8, 2) = (8 x 7) / (2 x 1).
Step 8: Calculate the numerator: 8 x 7 = 56.
Step 9: Calculate the denominator: 2 x 1 = 2.
Step 10: Divide the numerator by the denominator: 56 / 2 = 28.
Step 11: Conclude that there are 28 different ways to select 2 students from a class of 8.

Combinations – The concept of combinations is used to determine the number of ways to select items from a larger set where the order of selection does not matter.