A group consists of 5 boys and 6 girls. How many committees of 5 can be formed that consits of 2 boys 3 girls.
Multiple choice:
a)150
b) 200
c) 1800
d)2400
you want 2 from the 5 boys, and 3 from the 6 girsl
number of selections
= C(5,2) x C(6,3)
= .......
To find the number of committees that can be formed consisting of 2 boys and 3 girls out of a group of 5 boys and 6 girls, we can use the concept of combinations.
The number of ways to choose 2 boys out of 5 is denoted by "5C2" or "5 choose 2" and can be calculated using the formula:
5C2 = (5!)/(2!(5-2)!) = (5!)/(2!3!) = (5 × 4)/(2 × 1) = 10.
Similarly, the number of ways to choose 3 girls out of 6 is denoted by "6C3" and can be calculated as:
6C3 = (6!)/(3!(6-3)!) = (6!)/(3!3!) = (6 × 5 × 4)/(3 × 2 × 1) = 20.
To find the total number of committees that can be formed, we multiply the number of ways to choose boys with the number of ways to choose girls:
Total number of committees = 10 × 20 = 200.
Therefore, the correct answer from the multiple-choice options is b) 200.