There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys

Answer Details

To solve this problem, we need to use the combination formula: nCr = n! / r!(n-r)! where n is the total number of objects, r is the number of objects we want to select, and ! represents factorial, which means the product of all positive integers up to and including that number. In this problem, we want to select 3 girls and 2 boys out of 20 students, where 13 are girls and 7 are boys. The number of ways to select 3 girls out of 13 is: 13C3 = 13! / 3!(13-3)! = 13! / 3!10! = (13x12x11) / (3x2x1) = 286 Similarly, the number of ways to select 2 boys out of 7 is: 7C2 = 7! / 2!(7-2)! = 7! / 2!5! = (7x6) / (2x1) = 21 To find the total number of ways to select 3 girls and 2 boys out of 20, we need to multiply the number of ways to select 3 girls and 2 boys: 286 x 21 = 6006 Therefore, there are 6006 ways to select 3 girls and 2 boys from a class of 20. Hence, the correct answer is option (C) 6006.