How many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

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Question: How many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

Options:

Correct Answer: 60

Solution:

The number of ways = 5C2 * 4C2 = 10 * 6 = 60.

How many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

How many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

Step 1: Understand that we need to select 2 boys from a group of 5 boys.
Step 2: Use the combination formula to find the number of ways to choose 2 boys from 5. This is written as 5C2.
Step 3: Calculate 5C2. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 4: For 5C2, calculate it as 5! / (2!(5-2)!) = 5! / (2! * 3!) = (5*4)/(2*1) = 10.
Step 5: Now, understand that we also need to select 2 girls from a group of 4 girls.
Step 6: Use the combination formula to find the number of ways to choose 2 girls from 4. This is written as 4C2.
Step 7: Calculate 4C2 using the same combination formula: 4C2 = 4! / (2!(4-2)!) = 4! / (2! * 2!) = (4*3)/(2*1) = 6.
Step 8: Now, multiply the number of ways to choose the boys by the number of ways to choose the girls: 10 (ways to choose boys) * 6 (ways to choose girls) = 60.
Step 9: Conclude that there are 60 different ways to select 2 boys and 2 girls from the groups.

Combination – 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 also tests the application of the multiplication principle, where the total number of ways to choose items from different groups is the product of the number of ways to choose from each group.