How many ways can 2 boys and 3 girls be selected from a group of 6 boys and 8 gi

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Question: How many ways can 2 boys and 3 girls be selected from a group of 6 boys and 8 girls? (2020)

Options:

Correct Answer: 280

Exam Year: 2020

Solution:

The number of ways is 6C2 * 8C3 = 15 * 56 = 840.

How many ways can 2 boys and 3 girls be selected from a group of 6 boys and 8 girls? (2020)

How many ways can 2 boys and 3 girls be selected from a group of 6 boys and 8 girls? (2020)

Step 1: Understand that we need to select 2 boys from a group of 6 boys.
Step 2: Use the combination formula to find the number of ways to choose 2 boys from 6. This is written as 6C2.
Step 3: Calculate 6C2 using the formula: 6C2 = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6*5)/(2*1) = 15.
Step 4: Now, we need to select 3 girls from a group of 8 girls.
Step 5: Use the combination formula to find the number of ways to choose 3 girls from 8. This is written as 8C3.
Step 6: Calculate 8C3 using the formula: 8C3 = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8*7*6)/(3*2*1) = 56.
Step 7: Multiply the number of ways to choose the boys and the girls together: 15 (ways to choose boys) * 56 (ways to choose girls) = 840.
Step 8: Conclude that there are 840 different ways to select 2 boys and 3 girls from the groups.

Combination – The concept of selecting 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.