Diners at a certain restaurant can choose either a soup or salad from

Question

Diners at a certain restaurant can choose either a soup or salad from 4 choices, an entree from 5 offerings, two side dishes from 5 options, and, finally, one of 4 dessert cakes. To the nearest whole number, how many months could a person eat at this restaurant without having to order the same meal twice? (Assume 30 days per month.)

A) 20
B) 27
C) 63
D) 160
E) 800

A) 20
B) 27
C) 63
D) 160
E) 800

raypohan · Answer

PLEASE CORRECT ME IF I'M WRONG

CHOICES OF FOOD = 4 X 5 X 5C2 X 4 = 80 X 10 = 800
NUMBER OF DAYS = 30

= 800/300 = ~27

Soumya200011 · Answer

Total choice available = 4C1 * 5C1 * 5C2 * 4C1 =800
without repetition no. of dishes available = 800/30=26.6 ~ 27(rounded to the nearest whole number)
So, B.

For more understanding of the concept tested, refer to https://gmatclub.com/forum/learn-when-t ... 62678.html

Archit3110 · Answer

total options one can order
4*5c1*5c2*4c1 = 800
800 options so in 30 days one can eat 800/30 ; ~ 27 dishes
option B

MathRevolution · Answer

Choice of food options:  ^4{C_1} * ^5{C_1} * ^5{C_2} * ^4{C_1}  =800

Number of days: 30

=>  \frac{800 }{ 30}  ≈ 27

Answer B

srinath77 · Answer

How it is 4C1 for salad or soup from four choices. isnt should be like this 4C1+4C1 ?

Samuel0709 · Answer

That would violate the last condition put forth in the question which says that no one meal should be ordered twice. i.e no repetition if you have 8 ways to pick from 4 items that mean one item would have to be picked twice. The whole meal would have a different arrangement but we would have to order the same soup or salad again. Hope i could clarify your qn

Vveeeeee · Answer

Hello, 
Can anyone please help me? The question states that you can select a salad or a soup from four options. So, per salad or per soup you have four options, right? So shouldn't it be 4c1 + 4c1? Or is it that you have 4 options which includes soup and salad both? 
Kindly reply!

Bunuel · Answer

"Diners at a certain restaurant can choose either a soup or salad from 4 choices" means that there are total of four options for soup or salad.

lecremeglace · Answer

One thing to note is that they don't necessarily restrict you from choosing the same side dish. So instead of 5 choose 2 = 10 options, you would have 15, but I digress.

For those that don't like to remember the combinations formula, this one's for you!

4 ways to choose a soup/salad * 5 ways to choose an entrée * 5 ways to choose the first side dish * 4 ways to choose the second side dish * 4 ways to choose dessert =
4 * 5 * 5 * 4 * 4 = 1600 options, but remember, whether we choose one side dish over the other first, doesn't matter, so we have to divide all our options to account for that pair. Therefore, there are 1600/2 = 800 options.

800 options/30 days in a month gives us 80/3 or approx. 27 (B)

All without explicitly using the combinations formula, even though it's hidden in plain sight.

bumpbot · Answer

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Diners at a certain restaurant can choose either a soup or salad from

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