Suppose that in a class there are 8 people, 5 boys and 3 girls. We want to choose a team of 3 people with 2 boys and 1 girl. How many different groups can be formed?
with the first girl
combinations of 5 boys taken 2 at a time
= 5!/[3!(2!)] = 5*4/2 = 10
another 10 with girl 2
another 10 with girl 3
so 30
thank you very much
To find the number of different groups that can be formed, we can use the concept of combinations.
To choose 2 boys out of 5, we can use the formula for combinations: C(n, r) = n! / (r!(n-r)!), where n is the total number of boys and r is the number of boys we want to choose.
In this case, we want to choose 2 boys out of 5, so n = 5 and r = 2. Using the combination formula:
C(5, 2) = 5! / (2!(5-2)!) = 5! / (2!3!) = (5 * 4 * 3!) / (2! * 3!) = 10.
So, there are 10 different ways to choose 2 boys out of a group of 5.
To choose 1 girl out of 3, we can use the same combination formula:
C(3, 1) = 3! / (1!(3-1)!) = 3! / (1!2!) = (3 * 2 * 1!) / (1! * 2!) = 3.
So, there are 3 different ways to choose 1 girl out of a group of 3.
Now, to find the total number of different groups that can be formed, we multiply the number of ways to choose 2 boys with the number of ways to choose 1 girl:
10 * 3 = 30.
Therefore, there are 30 different groups that can be formed with 2 boys and 1 girl out of a class of 8 people.