(i) In a class with 8 boys and 11 girls, how many 5-member committees can be chosen
that have 4 girls?
there are 11C8 ways to select 4 girls from 11
there are 8 ways to select one boy from 8
multiply the results together to find the number of possible groupings
To find the number of committees that can be chosen with 4 girls out of 5 members in a class with 8 boys and 11 girls, we can use the concept of combinations.
First, we need to choose 4 girls out of the 11 available girls. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n - r)!)
Where C(n, r) represents the number of combinations of selecting r items from a set of n items.
So, the number of ways to choose 4 girls out of 11 is:
C(11, 4) = 11! / (4! * (11 - 4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)
= 330
Now, we have 4 girls selected, and we need to select 1 boy from the remaining 8 boys. This selection can be done in 8 ways.
Therefore, the total number of committees that can be chosen with 4 girls and 1 boy is:
330 * 8 = 2640
Hence, there are 2640 committees that can be chosen with 4 girls out of 5 members in the given class.