Question

I really need help!!!

Answer 1

Answer:

$Pr = 6.67\%$

Step-by-step 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:

$Pr = \frac{r}{n}$

$Pr = \frac{3! * 8!}{10!}$

Expand

$Pr = \frac{3*2*1 * 8!}{10*9*8!}$

$Pr = \frac{3*2*1}{10*9}$

$Pr = \frac{6}{90}$

$Pr = 0.0667$

Express as percentage

$Pr = 0.0667 * 100\%$

$Pr = 6.67\%$