How many ways can 2 boys and 2 girls be selected from 6 boys and 4 girls?
Practice Questions
Q1
How many ways can 2 boys and 2 girls be selected from 6 boys and 4 girls?
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Questions & Step-by-Step Solutions
How many ways can 2 boys and 2 girls be selected from 6 boys and 4 girls?
Correct Answer: 90
Step 1: Understand that we need to select 2 boys from a group of 6 boys.
Step 2: Use the combination formula C(n, k) which means 'n choose k'. Here, n is the total number of items to choose from, and k is the number of items to choose.
Step 3: Calculate C(6, 2) which is the number of ways to choose 2 boys from 6. The formula is C(6, 2) = 6! / (2! * (6-2)!) = 15.
Step 4: Now, we need to select 2 girls from a group of 4 girls.
Step 5: Calculate C(4, 2) which is the number of ways to choose 2 girls from 4. The formula is C(4, 2) = 4! / (2! * (4-2)!) = 6.
Step 6: Multiply the number of ways to choose boys and girls together: 15 (ways to choose boys) * 6 (ways to choose girls) = 90.
Step 7: Conclude that there are 90 different ways to select 2 boys and 2 girls from the groups.
