How many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?
Practice Questions
Q1
How many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?
60
40
50
30
Questions & Step-by-Step Solutions
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.
