Question

A and b stand in a line at random with 8 other people. what is the probability that there are exactly 3 people between a and b?

Answer 1

hey dear,
asylum here

a and b in a line and 8 other people
so no. of people =10
3+a and b= 5
probability = 5/10=1/2ans

Answer 2

Answer:

The probability that there are exactly 3 people between a and b is $\frac{2}{15}$

Step-by-step explanation:

Given : a and b stand in a line at random with 8 other people.

To find : What is the probability that there are exactly 3 people between a and b?

Solution :

Total number of positions are 10 i.e. 8 + position of a and b.

So, a and b can stand in a line $10\times 9$ ways as if a position is fix b have to take another.

i.e. The sample space consist of all possible ways of standing is  $10\times 9=90$

Now, There are exactly 3 people between a and b.

i.e. The position of a and b can be arranged in a positions  (1,5), (2,6), (3,7), (4,8), (5,9), (6,10) as there is 3 vacant space between them.

Outcomes are 6.

As a and b can interchange their positions so favorable outcomes were,

Favorable outcomes $2\times 6=12$

The probability that there are exactly 3 people between a and b is

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcomes}}$

$\text{Probability}=\frac{12}{90}$

 $\text{Probability}=\frac{2}{15}$

Therefore, The probability that there are exactly 3 people between a and b is $\frac{2}{15}$