# Homework Help: How many different Lunches from the Lunch Menu

1. Aug 13, 2017

### zak100

1. The problem statement, all variables and given/known data
A diner serves a lunch special, consisting of soup or salad, a sandwich, coffee or tea and a dessert. If the menu lists 3 soups , 2 salads, 7 sandwiches and 8 desserts, how many different lunches can you choose?

2. Relevant equations
Counting Principle

3. The attempt at a solution
Sandwiches = 7
Deserts = 8
The above two are without 'or' so their combinations = 56.
Combining 2 Salads = 56 * 2 = 112
or Combining 3 soups = 56 * 3 = 168
Total = 112 + 168 = 280

Zulfi.

2. Aug 13, 2017

### phinds

what is 5x7x2x8 ?

3. Aug 13, 2017

### zak100

Hi,
I know about 7, 2 & 8 but i dont know whats 5?

Zulfi.

4. Aug 13, 2017

### SammyS

Staff Emeritus
You are missing one choice.

5. Aug 13, 2017

### zak100

Hi,
Are you talking about tea and coffee? No quantity mentioned about them so i have not included them.

Zulfi.

6. Aug 13, 2017

### SammyS

Staff Emeritus
Yes. That's what I'm referring to.

7. Aug 13, 2017

### Ray Vickson

It said that each meal includes either tea or coffee, so you cannot neglect them.

8. Aug 13, 2017

### phinds

5 = 3 + 2

9. Aug 13, 2017

### haruspex

In case it is not clear from the previous replies, you have two errors. Ray and Sammy are pointing out that you have omitted the tea/coffee choice, while phinds is drawing attention to the fact that soup and salad are mutually exclusive.

10. Aug 15, 2017

### zak100

Hi,
Thanks all for your help. Tea/Coffee: what is their quantity? If i say that each is one, then there is no effect. I dont know what you mean by mutual Exclusive. In computer this is used for shareable device used one at a time.

Zulfi.

11. Aug 15, 2017

### haruspex

It means you cannot have both. It says "soup or salad". If there are 3 soups and two salads, how many different things can you choose?
You can have tea or coffee. How many different things can you choose?

12. Aug 15, 2017

### zak100

Hi,
<It means you cannot have both. It says "soup or salad". If there are 3 soups and two salads, how many different things can you choose?>
If there are 3 soups S1, S2 & S3 & 2 Salads C1, C2 then it means i cant have:
S1C1, S1C2, S2C1, S2C2, S3C1, S3C2
So i have to take each of them alone so there are 5 five choices now:
S1, S2, S3, C1, C2 and tea or coffee, i have 2 choices:
Tea1, Coffee1
7 * 8 * 5 * 2 = 560
Thanks.
Zulfi.

13. Aug 15, 2017

### haruspex

Good.

14. Aug 15, 2017

### phinds

Exactly. See post #2 in which my point was that you were making this problem harder than it is.

15. Aug 15, 2017

### zak100

Yes my friend, thanks for your response. Actually i already have the solution, but i cant understand it so i was looking for more details.

Zulfi.