How many different Lunches from the Lunch Menu

[zak100]

Homework Statement

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?

Homework Equations

Counting Principle

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

but answer is wrong. Some body please guide me.

Zulfi.

 

[phinds]

what is 5x7x2x8 ?

 

[zak100]

Hi,
I know about 7, 2 & 8 but i don't know what's 5?

Zulfi.

 

[SammyS]

Homework Statement

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?

Homework Equations

Counting Principle

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

but answer is wrong. Some body please guide me.

Zulfi.

You are missing one choice.

 

[zak100]

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

Zulfi.

 

[SammyS]

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

Zulfi.

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

 

[Ray Vickson]

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

Zulfi.

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

 

[phinds]

5 = 3 + 2

 

[haruspex]

but answer is wrong. Some body please guide me.

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.

 

[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 don't know what you mean by mutual Exclusive. In computer this is used for shareable device used one at a time.
Please guide me.

Zulfi.

 

[haruspex]

dont know what you mean by mutual Exclusive

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?

Tea/Coffee: what is their quantity?

You can have tea or coffee. How many different things can you choose?

 

[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 can't 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.

 

[haruspex]

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 can't 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.

Good.

 

[phinds]

7 * 8 * 5 * 2.

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

 

[zak100]

Yes my friend, thanks for your response. Actually i already have the solution, but i can't understand it so i was looking for more details.

Zulfi.