zulfi100

Joined Jun 7, 2012
656
Hi,
I have got following question which i cant solve:

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?

My solution is:

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.

Raymond Genovese

Joined Mar 5, 2016
1,653
What drink will you have in those 280 meals?

zulfi100

Joined Jun 7, 2012
656
What drink will you have in those 280 meals?
Hi,

3 soups. There is no quantity mentioned about tea & coffee, so i am not considering them.

Zulfi.

Raymond Genovese

Joined Mar 5, 2016
1,653
Hi,

3 soups. There is no quantity mentioned about tea & coffee, so i am not considering them.

Zulfi.
As I read the problem, not considering coffee or tea is why you are not getting the right answer. You may be getting tricked by the wording...what if it were phrased as two kinds of drinks?

"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?"

Lunch=(soup or salad)+sandwich+(coffee or tea) + dessert. Right?

WBahn

Joined Mar 31, 2012
28,517
Consider the following rephrase:

Your meal consists of one choice for each of the following four items: appetizer, entrée, drink, dessert.

Your appetizer can be one of our three soups or one of our two salads.
Your entrée can be one of our seven sandwiches.
Your drink can be either tea or coffee.
Your dessert can be one of our eight desserts.

How many options does the person have for each of the four items.

How many possible combinations of them are there?

zulfi100

Joined Jun 7, 2012
656
Hi,
<Your appetizer can be one of our three soups or one of our two salads.>

Let the soups be: S1, S2, S3 & Salads be: C1, C2
Combinations: S1C1, S2C1, S3C1, S1C2, S2C2, S3C2.
There are 6 combinations.
Zulfi.

RBR1317

Joined Nov 13, 2010
706
There are 6 combinations.
But if your choice of appetizer is soup or salad then you only get one item, not a combination of items.

WBahn

Joined Mar 31, 2012
28,517
Hi,
<Your appetizer can be one of our three soups or one of our two salads.>

Let the soups be: S1, S2, S3 & Salads be: C1, C2
Combinations: S1C1, S2C1, S3C1, S1C2, S2C2, S3C2.
There are 6 combinations.
Zulfi.

How many different selections can you make?

To make it even more practical:

Appetizer Menu: Choose one of the following:
Soups: Tomato, Mushroom, Chicken Noodle

How many appetizer selections do you have?

zulfi100

Joined Jun 7, 2012
656
Hi,
Thanks for your response. I am able to solve this prob.

Actually i was doing mistake here, and it slipped from your attention:
<
Let the soups be: S1, S2, S3 & Salads be: C1, C2
Combinations: S1C1, S2C1, S3C1, S1C2, S2C2, S3C2.
There are 6 combinations.
>
There would be 5 combinations not 6.
Zulfi.

Raymond Genovese

Joined Mar 5, 2016
1,653
Hi,
Thanks for your response. I am able to solve this prob.

Actually i was doing mistake here, and it slipped from your attention:
<
Let the soups be: S1, S2, S3 & Salads be: C1, C2
Combinations: S1C1, S2C1, S3C1, S1C2, S2C2, S3C2.
There are 6 combinations.
>
There would be 5 combinations not 6.
Zulfi.

zulfi100

Joined Jun 7, 2012
656
Hi,
I wrote this earlier:
S1C1, S1C2, S2C1, S2C2, S3C1, S3C2
but its not correct. It says soup or salad. I cant have both. So i have to take each of them alone so there are 5 choices now:

S1, S2, S3, C1, C2

and similarly for tea or coffee, i cant have both so there are two choices:
Tea , coffee
7 * 8 * 5 * 2 = 560
Thanks.
Zulfi.

Raymond Genovese

Joined Mar 5, 2016
1,653
Hi,
I wrote this earlier:
S1C1, S1C2, S2C1, S2C2, S3C1, S3C2
but its not correct. It says soup or salad. I cant have both. So i have to take each of them alone so there are 5 choices now:

S1, S2, S3, C1, C2

and similarly for tea or coffee, i cant have both so there are two choices:
Tea , coffee
7 * 8 * 5 * 2 = 560
Thanks.
Zulfi.
Yes, you do have it! Good deal.

WBahn

Joined Mar 31, 2012
28,517
Hi,
Thanks for your response. I am able to solve this prob.

Actually i was doing mistake here, and it slipped from your attention:
<
Let the soups be: S1, S2, S3 & Salads be: C1, C2
Combinations: S1C1, S2C1, S3C1, S1C2, S2C2, S3C2.
There are 6 combinations.
>
There would be 5 combinations not 6.
Zulfi.
How did it slip from our attention? Both RBR1317 and I promptly indicated an issue with this claim.