In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
The team can be selected in 40 ways.
Explanation
This is a combination problem where we need to select a specific number of boys and girls. The context shows similar problems solved using the multiplication principle with combinations. For example, selecting '3 girls and 2 boys can be selected in ^{4}C_{3} × ^{7}C_{2} ways.' Applying this same method, we multiply the number of ways to select boys by the number of ways to select girls.
Solution Steps
Step 1: Number of ways to select 3 boys from 5 boys = ^{5}C_{3} = 5!/(3! × 2!) = ()/2 = 10
Step 2: Number of ways to select 3 girls from 4 girls = ^{4}C_{3} = 4!/(3! × 1!) = 4
Step 3: By multiplication principle, total number of ways = ^{5}C_{3} × ^{4}C_{3} = = 40