How many ways can 2 boys and 3 girls be selected from 6 boys and 4 girls? (2023)

How many ways can 2 boys and 3 girls be selected from 6 boys and 4 girls? (2023)

Step 1: Identify the total number of boys and girls available. We have 6 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 to find the number of ways to select 2 boys from 6. This is calculated as 6C2.
Step 4: Calculate 6C2. The formula for combinations is nCr = n! / (r!(n-r)!). So, 6C2 = 6! / (2!(6-2)!) = 6! / (2! * 4!) = (6*5)/(2*1) = 15.
Step 5: Now, determine how many girls we need to select. We need to select 3 girls.
Step 6: Use the combination formula to find the number of ways to select 3 girls from 4. This is calculated as 4C3.
Step 7: Calculate 4C3. Using the combination formula, 4C3 = 4! / (3!(4-3)!) = 4! / (3! * 1!) = 4.
Step 8: Multiply the number of ways to select boys by the number of ways to select girls. This gives us the total number of ways to select 2 boys and 3 girls: 15 * 4.
Step 9: Calculate the final result: 15 * 4 = 60.

Combination – The concept of selecting a subset of items from a larger set without regard to the order of selection, represented mathematically as nCr.
Binomial Coefficient – The formula used to calculate combinations, which is n! / (r!(n-r)!), where n is the total number of items, and r is the number of items to choose.