Question

I really need help!!!

Jason, Lewis, and Nora will be placed in a line along with 7 other people.


What is the probability that they will be next to each other in any order?
Give percentage

Answer 1

`Pr = 6.67\%`

Explanation:

Given

`n = 10` i.e. 10 people

Required

Probability of being next to each other

First, we calculate the total possible arrangements (without any restriction)

`Total = n!`

`Total = 10!`

If the three are to be next to each other,

First, we arrange the three

`r_1 = 3!`

Now, the 3 will be seen as 1; so, we have a total of 8 people i.e. (1 + 7 others)

The arrangement is:

`r_2 =8!`

So, the total arrangement, when they have to be next to one another is:

`r = r_1 * r_2`

`r = 3! * 8!`

The probability is:

`Pr = (r)/(n)`

`Pr = (3! * 8!)/(10!)`

Expand

`Pr = (3*2*1 * 8!)/(10*9*8!)`

`Pr = (3*2*1)/(10*9)`

`Pr = (6)/(90)`

`Pr = 0.0667`

Express as percentage

`Pr = 0.0667 * 100\%`

`Pr = 6.67\%`