# Question #26b22

##### 2 Answers

Use the **complement method** for an easy solution.

#### Explanation:

First, determine the number of ways that 4 and 5 ARE next to each other:

45xxxx

x45xxx

xx45xx

xxx45x

xxxx45

So, these 5 ways plus the 5 reverse ways where 5 precedes 4.

In total, there are 10 ways that the numbers 4 and 5 are next to each other. However, there are still 4! = 24 ways to arrange the remaining 4 numbers. So, there are **ARE** next to each other .

In general, there are 6! = 720 ways to arrange the 6 numbers.

Using the **complement method** :

P(4 and 5 **not** next to each other)

Hope that helped

Prob. that 4 and 5 are always next to each other is

Probability that cards numbered 4 and 5 are not next to each other is 1 - 1/3 = 2/3.

#### Explanation:

The events in question are complements.