from a handpicked tutor in LIVE 1-to-1 classes

# 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: The teacher can select 1 boy and 1 girl to represent the class at a seminar, in 150 different ways.

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

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

= 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 teacher can select 1 boy and 1 girl to represent the class at a seminar in 150 different ways.

visual curriculum