How many different ways can 2 boys and 2 girls be selected from a group of 5 boy

How many different ways can 2 boys and 2 girls be selected from a group of 5 boys and 4 girls?

How many different ways can 2 boys and 2 girls be selected from a group of 5 boys and 4 girls?

Correct Answer: 60

Step 1: Identify the total number of boys and girls. We have 5 boys and 4 girls.
Step 2: Determine how many boys we need to select. We need to select 2 boys.
Step 3: Use the combination formula C(n, r) to find the number of ways to choose 2 boys from 5. This is calculated as C(5, 2).
Step 4: Calculate C(5, 2). The formula is C(n, r) = n! / (r! * (n - r)!). So, C(5, 2) = 5! / (2! * (5 - 2)!) = 10.
Step 5: Now, determine how many girls we need to select. We need to select 2 girls.
Step 6: Use the combination formula C(4, 2) to find the number of ways to choose 2 girls from 4. This is calculated as C(4, 2).
Step 7: Calculate C(4, 2). Using the same formula, C(4, 2) = 4! / (2! * (4 - 2)!) = 6.
Step 8: Multiply the number of ways to choose boys by the number of ways to choose girls. So, we calculate 10 (from boys) * 6 (from girls) = 60.
Step 9: The final answer is that there are 60 different ways to select 2 boys and 2 girls from the group.

Combination – The concept of selecting a subset of items from a larger set without regard to the order of selection.
Binomial Coefficient – The mathematical notation C(n, k) represents the number of ways to choose k elements from a set of n elements.