How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 6 gi

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Question: How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 6 girls?

Options:

Correct Answer: 100

Solution:

The number of ways is C(5, 2) * C(6, 3) = 10 * 20 = 200.

How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 6 girls?

How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 6 girls?

Correct Answer: 200

Step 1: Identify the total number of boys and girls in the group. There are 5 boys and 6 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 for combinations 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 3 girls.
Step 6: Use the combination formula C(n, r) to find the number of ways to choose 3 girls from 6. This is calculated as C(6, 3).
Step 7: Calculate C(6, 3). Using the combination formula, C(6, 3) = 6! / (3! * (6 - 3)!) = 20.
Step 8: Multiply the number of ways to choose the boys by the number of ways to choose the girls. This gives us the total number of ways to select 2 boys and 3 girls: 10 * 20 = 200.

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.