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A restaurant serves 6 varieties of appetizers, 10 different entrees an
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24 Jun 2015, 10:42
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A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert? A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\) B) 6*10*4 C) 6*10*2*4 D) 6*9*4 E) \(\frac{6*10*4}{2}\)
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Re: A restaurant serves 6 varieties of appetizers, 10 different entrees an
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24 Jun 2015, 10:50



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Re: A restaurant serves 6 varieties of appetizers, 10 different entrees an
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24 Jun 2015, 10:57
Bunuel wrote: Patronus wrote: A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?
A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\) B) 6*10*4 C) 6*10*2*4 D) 6*9*4 E) \(\frac{6*10*4}{2}\) 1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\); 1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\). Total = A. Answer: A. Thank you for the short answer Bunuel. Can you please tell me why we should use \(\frac{(10*9)}{2}\) and not 10*9? I solved it by thinking we have to fill 2 spots out of 10 contenders (entrees). Therefore, first spot can be filled in 10 ways and the 2nd spot in 9 ways. Sorry, but I normally get confused with when to use Combinations and Permutations. Can you please clarify?
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Re: A restaurant serves 6 varieties of appetizers, 10 different entrees an
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24 Jun 2015, 11:03
Patronus wrote: Bunuel wrote: Patronus wrote: A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?
A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\) B) 6*10*4 C) 6*10*2*4 D) 6*9*4 E) \(\frac{6*10*4}{2}\) 1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\); 1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\). Total = A. Answer: A. Thank you for the short answer Bunuel. Can you please tell me why we should use \(\frac{(10*9)}{2}\) and not 10*9? I solved it by thinking we have to fill 2 spots out of 10 contenders (entrees). Therefore, first spot can be filled in 10 ways and the 2nd spot in 9 ways. Sorry, but I normally get confused with when to use Combinations and Permutations. Can you please clarify? \(C^2_{10}\), which is 10*9/2 is the number of two entrees possible when the order of entrees does not matter. \(P^2_{10}\), which is 10*9 is the number of two entrees possible when the order of entrees matters, i.e. when we differentiate between (entree X, entrees Y) from (entree Y, entrees X).
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A restaurant serves 6 varieties of appetizers, 10 different entrees an
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25 Jun 2015, 01:39
Bunuel wrote: Patronus wrote: A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?
A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\) B) 6*10*4 C) 6*10*2*4 D) 6*9*4 E) \(\frac{6*10*4}{2}\) 1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\); 1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\). Answer: A. Hi Bunnel, Why is there (+) in choice A? what does it mean? what not multiplication sign (*)? Thanks



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Re: A restaurant serves 6 varieties of appetizers, 10 different entrees an
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25 Jun 2015, 02:15
Mo2men wrote: Bunuel wrote: Patronus wrote: A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?
A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\) B) 6*10*4 C) 6*10*2*4 D) 6*9*4 E) \(\frac{6*10*4}{2}\) 1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\); 1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\). Answer: A. Hi Bunnel, Why is there (+) in choice A? what does it mean? what not multiplication sign (*)? Thanks Principle of MultiplicationIf an operation can be performed in ‘m’ ways and when it has been performed in any of these ways, a second operation that can be performed in ‘n’ ways then these two operations can be performed one after the other in ‘m*n’ ways. Principle of AdditionIf an operation can be performed in ‘m’ different ways and another operation in ‘n’ different ways then either of these two operations can be performed in ‘m+n’ ways ( provided only one has to be done).
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: A restaurant serves 6 varieties of appetizers, 10 different entrees an
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02 Sep 2017, 14:48
Patronus wrote: A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?
A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\) B) 6*10*4 C) 6*10*2*4 D) 6*9*4 E) \(\frac{6*10*4}{2}\) There's two basic scenarios 6c1 x 10c1 x 4c1 = [6 x 10 x 4] 6c1 x 10c2 x 4c1 = [6 x 45 x 4] Account for both possibilities hence How many possibilities with 10c1 + how many possibilities with 10c2 [6 x 10 x 4] + [6 x 45 x 4] A




Re: A restaurant serves 6 varieties of appetizers, 10 different entrees an &nbs
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