How many ways can 2 boys and 2 girls be selected from a group of 5 boys and 5 gi
Practice Questions
Q1
How many ways can 2 boys and 2 girls be selected from a group of 5 boys and 5 girls? (2023)
100
120
80
60
Questions & Step-by-Step Solutions
How many ways can 2 boys and 2 girls be selected from a group of 5 boys and 5 girls? (2023)
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. The formula 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 3: For boys, n = 5 and r = 2. Calculate 5C2: 5! / (2!(5-2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.
Step 4: Now, understand that we also need to select 2 girls from a group of 5 girls.
Step 5: Use the same combination formula for girls. For girls, n = 5 and r = 2. Calculate 5C2: 5! / (2!(5-2)!) = 10 (same calculation as for boys).
Step 6: Now, multiply the number of ways to choose boys by the number of ways to choose girls: 10 (ways to choose boys) * 10 (ways to choose girls) = 100.
Step 7: Conclude that there are 100 different ways to select 2 boys and 2 girls from the groups.
