For a quiz competition, a group of 3 students is selected randomly from a class consisting of 5 boys and 5 girls. What is the probability that one girl and two boys are selected?
Answers
Answer:
1/10 is the probability
Given,
The number of students in a group = 3
The number of boys = 5
The number of girls = 5
To Find,
The probability that one girl and two boys are selected =?
Solution,
The total students = 5 + 5 = 10
The number of ways of selecting 3 students from 10 students = 10C3
The number of ways of selecting 3 students from 10 students = 10! / (3!*7!)
The number of ways of selecting 3 students from 10 students =(10*9*8)/3*2
The number of ways of selecting 3 students from 10 students = 120 ways
The number of ways of selecting 2 boys from 5 boys = 5C2
The number of ways of selecting 2 boys from 5 boys = 5!/(3!*2!)
The number of ways of selecting 2 boys from 5 boys = 5 * 4 / 2
The number of ways of selecting 2 boys from 5 boys =10 ways
The number of ways of selecting 1 girl from 5 girls =5!/(4!*1!)
The number of ways of selecting 2 boys from 5 boys = 5 ways
Total ways of selecting one girl and two boys = 5 * 10
Total ways of selecting one girl and two boys = 50 ways
The probability that one girl and two boys are selected = 50 / 120
The probability that one girl and two boys are selected = 5 / 12
Hence, the probability that one girl and two boys are selected is 5/12.