There are 10 boys and 13 girls in Mr. Benson\'s fourth-grade class. A picnic com
ID: 3205404 • Letter: T
Question
There are 10 boys and 13 girls in Mr. Benson's fourth-grade class. A picnic committee of six students is selected at random from the students in the class. How many ways arc there to select a committee with only girls? How many ways are there to select a committee with six students? What is the probability that all the committee members are girls? What is the probability that the committee has three girls and three boys? What is the probability that the committee has at most 3 girls in the committeeExplanation / Answer
Solution:
We are given total number of students = 10 boys + 13 girls = 23
We have to select a committee of six students.
Part a
Total number of girls = 13
Number of students in committee = 6
Required number of ways to select a committee with only girls = 13C6
Required number of ways = 13!/(13 – 6)!6! = 1716
Answer = 1716
Part b
Total number of students = 23
Number of students in committee = 6
Required number of ways to select a committee = 23C6
Required number of ways = 23! / (23 – 6)!6! = 100947
Answer = 100947
Part c
Here, we have to find the probability that all the committee members are girls.
Total number of ways for selecting six students = 100947
Total number of ways for selecting all six girls = 1716
Required probability = 1716 / 100947 = 0.016999
Answer = 0.016999
Part d
Here, we have to find the probability that the committee has three girls and three boys.
We can select 3 girls from 13 girls in 13C3 ways.
We can select 3 boys from 10 boys in 10C3 ways.
We can select the committee of three girls and three boys in 13C3*10C3 ways.
Total number of ways for selection of committee = 13C3*10C3 = [13!/(13 – 3)!3!]*[10!/(10 – 3)!3!]
Total number of ways for selection of committee = 286*120 = 34320
Total number of ways for selecting six students = 100947
Required probability = 34320 / 100947 = 0.33998
Answer = 0.33998
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