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A restaurant has a set menu that consists of three courses

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A restaurant has a set menu that consists of three courses [#permalink]

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13 Oct 2006, 08:05
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A restaurant has a set menu that consists of three courses and a choice of beverages. The first course is a choice of leek soup, smoked salmon salad or fried eggplant. The second course is a choice of grilled sole, beef stew, canelloni, or rice with clams. The third course is a choice of fruit salad, ice cream or yoghurt with honey. The owner of the restaurant boasts that, if a dish for at least two courses and one beverage are ordered, a different meal can be had every day of an entire year. What is the least number of beverages that she must offer so that this claim is true?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
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13 Oct 2006, 08:59
I will go with 6 i.e option B.

I course contain 3 varieties
II course contain 4 varieties
III course contain 3 varieties
Suppose there are p beverages .

We have to order a dish for atleat two courses and one beverage.

Case 1 Exactly 2 courses and one beverage
These 2 courses again could be from
I ,II or II, III or I, III

So this will be 3C1x4C1xpC1 + 4C1x3C1xpC1 + 3C1x3C1xpC1
i.e 12p+12p+9p = 33p

Case 2: Exactly 3 courses and one beverage.
This will be 3C1x4C1x3C1xpC1 = 36p

So 33p+36p=365
i.e 69p=365
So p>5
So minimum 6 beverages must be offered
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13 Oct 2006, 10:40
Didn't understand question initially. Followed cicerone's line of reasoning.
He seems to be right. GOOD WORK CICERONE.

Kevin, OA on this please. And do you more from where this came from?
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13 Oct 2006, 13:47
Rayn wrote:
Didn't understand question initially. Followed cicerone's line of reasoning.
He seems to be right. GOOD WORK CICERONE.

Kevin, OA on this please. And do you more from where this came from?

Cicerone's solution is correct! These questions come out of what's left of my brain after a hard day's work! I have been teaching counting methods and I was hungry in class, which explains the elaborate menu!
13 Oct 2006, 13:47
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