How Many Ways a Teacher Can Select 1 Boy and 1 Girl to Represent the Class at a Seminar?


Question: In class, there are 15 boys and 10 girls. How many ways a teacher can select 1 boy and 1 girl to represent the class at a seminar?

Probability is defined as how likely an event is to occur

Answer: 1/2 is the probability that a teacher can select 1 boy and 1 girl to represent the class at a seminar.

nCr represents the selection of objects from a group of objects. nCr= n!/[r! (n-r)!], Where n is the total number of objects and r is the number of selected objects.

Explanation:

There are 15 boys and 10 girls

In total = 15 + 10 = 25

The number of ways to select 2 members out of 25 is 25c2 = 25! / [(25 - 2)! × 2!]

                                                                                               = 25! / [23! × 2!]

                                                                                               = 25 × 24 × 23! / 23! × 2!

                                                                                               = 25 × 24 / 2 = 25 × 12 = 300

The number of ways to select 1 boy and 1 girl = (15c1) × (10c1)

                                                                            = 15! / [(15 - 1)! × 1!] × 10! / [(10 - 1)! × 1!]

                                                                            = 15! / [14! × 1!]  × 10! / [9! × 1!]

                                                                            = 15 x 14! / [14!]  x  10 × 9! /[ 9! × 1]

                                                                            = 15 × 10

                                                                            = 150

The probability to select 1 boy and 1 girl = 150 / 300 = 1/2

Therefore, the probability that a teacher can select 1 boy and 1 girl to represent the class at a seminar is 1/2.