Chapter 9.1, Problem 37E

Solution

To state: The number of different lunches that can be created by Mary if she can choose among nine different salads.

The resultant value is 511 lunch.

Given information:

Mary can choose among nine different salads. She has two options she can either pick a salad or not.

Explanation:

The total number of salad options is 9. She can either pick a salad or not.

For the first salad option has 2 possibilities. Similarly for the second salad option, again there are 2 possibilities. Thus it can be said that for each salad option there are 2 possibilities.

The total number of ways in which the 9 salads can be chosen is:

  $2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2=512$

The number of ways in which no salad is selected is: 1

Then the number of ways in which different can be selected by Mary is:

  $512-1=511$

Therefore, there are 511 ways in which Mary can select her lunch.