How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls? (2020)
Practice Questions
Q1
How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls? (2020)
100
150
200
300
Questions & Step-by-Step Solutions
How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls? (2020)
Step 1: Understand that we need to select 2 boys from a group of 5 boys.
Step 2: Use the combination formula C(n, r) to find the number of ways to choose r items from n items. Here, n is 5 (boys) and r is 2 (boys to select).
Step 3: Calculate C(5, 2) using the formula: C(n, r) = n! / (r! * (n - r)!). For C(5, 2), it is 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.
Step 4: Now, repeat the same process for the girls. We need to select 2 girls from 5 girls, so we again calculate C(5, 2). This will also be 10.
Step 5: To find the total number of ways to select 2 boys and 2 girls, multiply the number of ways to select boys by the number of ways to select girls: Total = C(5, 2) * C(5, 2) = 10 * 10 = 100.
