Question: How many ways can 2 boys and 2 girls be selected from 6 boys and 4 girls?
Options:
60
30
40
50
Correct Answer: 60
Solution:
The number of ways is C(6,2) * C(4,2) = 15 * 6 = 90.
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?
60
30
40
50
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.
Combination – The concept of selecting items from a larger set without regard to the order of selection, represented mathematically as C(n, k), where n is the total number of items and k is the number of items to choose.
Multiplication Principle – The principle that states if there are multiple independent choices to be made, the total number of ways to make those choices is the product of the number of ways to make each choice.
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