How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls? (2020)

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Question: How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls? (2020)

Options:

Correct Answer: 150

Exam Year: 2020

Solution:

The number of ways to select 2 boys from 5 is C(5, 2) and 2 girls from 5 is C(5, 2). Total = C(5, 2) * C(5, 2) = 10 * 10 = 100.

How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls? (2020)

How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls? (2020)

Step 1: Understand that we need to select 2 boys from a group of 5 boys.
Step 2: Use the combination formula C(n, r) to find the number of ways to choose r items from n items. Here, n is 5 (boys) and r is 2 (boys to select).
Step 3: Calculate C(5, 2) using the formula: C(n, r) = n! / (r! * (n - r)!). For C(5, 2), it is 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.
Step 4: Now, repeat the same process for the girls. We need to select 2 girls from 5 girls, so we again calculate C(5, 2). This will also be 10.
Step 5: To find the total number of ways to select 2 boys and 2 girls, multiply the number of ways to select boys by the number of ways to select girls: Total = C(5, 2) * C(5, 2) = 10 * 10 = 100.

Combinatorics – The question tests the understanding of combinations, specifically how to choose a subset of items from a larger set without regard to the order of selection.
Multiplication Principle – It assesses the application of the multiplication principle in counting, where the total number of ways to perform multiple independent selections is the product of the number of ways to perform each selection.