A college offers 5 different majors. If a student can choose 2 majors, how many

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Question: A college offers 5 different majors. If a student can choose 2 majors, how many different combinations are possible?

Options:

Correct Answer: 10

Solution:

Combinations = 5C2 = 5! / (2!(5-2)!) = 10.

A college offers 5 different majors. If a student can choose 2 majors, how many different combinations are possible?

A college offers 5 different majors. If a student can choose 2 majors, how many different combinations are possible?

Step 1: Understand that we need to find combinations of 2 majors from 5 available majors.
Step 2: Use the combination formula, which is written as nCr, where n is the total number of items (majors) and r is the number of items to choose (majors). Here, n = 5 and r = 2.
Step 3: The combination formula is nCr = n! / (r!(n-r)!).
Step 4: Substitute the values into the formula: 5C2 = 5! / (2!(5-2)!).
Step 5: Calculate (5-2) which equals 3, so we have 5C2 = 5! / (2! * 3!).
Step 6: Calculate the factorials: 5! = 5 × 4 × 3 × 2 × 1 = 120, 2! = 2 × 1 = 2, and 3! = 3 × 2 × 1 = 6.
Step 7: Substitute the factorial values back into the equation: 5C2 = 120 / (2 * 6).
Step 8: Calculate the denominator: 2 * 6 = 12.
Step 9: Now divide: 120 / 12 = 10.
Step 10: Therefore, there are 10 different combinations of 2 majors from 5.

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 itself, denoted by n!.