Question

A judging panal of 7people is to be randomly selected from 8 teachers and 20 students.What is the probability that there are more students than teachers on the panal?

Answer 1

Solution:
Given in the question
Number of teachers = 8
Number of students = 20
Total number from which we need to select = 8+20 = 28
We need to choose 7 people and calculate the probability that there are more students than teachers on the panel
P(7 people so that there are more students than teachers on the panel) = Total number of ways to select 7 people like there are more students than teachers on the panel/ Total number of ways to select 7 people out of 28
Total number of ways to select 7 people out of 28 = 28C7 = 1184040
Number of cases to select 7 people to like to there are more students than teachers on the panel
Case 1: 4 student & 3 teachers
No. of ways = 20C4 * 8C3
Case 2: 5 Student & 2 teachers
No. of ways = 20C5*8C2
Case 3: 6 Student & 1 teachers
No. of ways = 20C6*8C1
Case 4: 7 student & 0 teachers
No. of ways = 20C7*8C0
Total number of ways to select 7 people to like to there are more students than teachers on the panel = 20C4*8C3 + 20C5*8C2 + 20C6*8C1 + 20C7*8C0 = 271320 + 434112 + 310080 + 77520 = 1093032
P(7 people so that there are more students than teachers on the panel) = 1093032 /1184040 = 0.9231
So there is 92.31% probability that there are more students than teachers on the panal.