Chapter 11.1, Problem 48PPSE

Solution

a.

To identify:Whether the order in which the videos are selected make a difference or not. If they have selected 7 videos but will only have time to watch 3 videos together.

No, order doesn’t matter.

Given information:

They have selected 7 videos but will only have time to watch 3 videos together.

Explanation:

Consider the given information.

They have 7 videos and all are different.

They have time to watch 3 videos together.

Here order doesn’t matter because they can see these three videos in any order.

Switching order doesn’t make any differences.

b.

To calculate: The number of ways in which they can select 3 videos to watch if theyand friends picking up videos at a video store together. Also mention the formula which can be used.They have selected 7 videos but will only have time to watch 3 videos together.

The required formula is: $C{}_r=\frac{n!}{\left(n-r\right)!r!}$ wheren is the total number of items taken r at a time. The resultant value is 35ways.

Given information:

It is given that friends have selected 7 videos but will only have time to watch 3 videos together.

Formula used: If $C{}_r$ represents the number of combinations of n items taken r at a time, then $C{}_r=\frac{n!}{\left(n-r\right)!r!}$ .

Calculation:

The order of the video selection does not matter, so the formula for combination must be used.

The number of ways in which 3 videos can be selected from a group of 7 videos,

  $C{}_3$

Rewrite the expression using the formula $C{}_r=\frac{n!}{\left(n-r\right)!r!}$ ,

  $\begin{array}{c}C{}_3=\frac{7!}{\left(7-3\right)!3!}\\ =\frac{10!}{4!3!}\end{array}$

Now expand the factorial,

  $\begin{array}{c}\frac{7\cdot 6\cdot 5\cdot 4!}{4!\left(3\cdot 2\cdot 1\right)}=\frac{7\cdot 6\cdot 5}{3\cdot 2}\\ =35\end{array}$

Therefore, there are 35 ways in which 3 videos to watch can be selected.