Rick’s Sandwich Shop lets customers create their own sandwiches by cho

Question

Rick’s Sandwich Shop lets customers create their own sandwiches by choosing from among a certain number of ingredients. When ordering Rick’s Rockin’ Sandwich, the customer must choose 1 of 3 breads, 1 of 6 meats, and 1 of 4 cheeses. The customer can also add up to 3 of 8 different veggies. How many unique Rick’s Rockin’ Sandwiches could a customer order?

A. 4,032

B. 6,624

C. 6,696

D. 24,192

E. 28,932

A. 4,032

B. 6,624

C. 6,696

D. 24,192

E. 28,932

Archit3110 · Accepted Answer

must choose
breads 3c1 ; 3
meats 6c1 ; 6
cheeses 4c1 ; 4
veggies can also be added condition ( conditional ) (0,1,2,3)
we get 4 cases
no veggies ;3*6*4 ; 72
1 veggie ; 72*8 ; 576
2 veggies ; 72*8c2 ; 2016
3 veggies ; 72* 8c3 ; 4032
total possiblities ; 72 +576+2016+4032 ; 6696
option C

logro · Answer

Total number of ways = 3C1*6C1*4C1*8C3 = 3*6*4*56 = 4032

Hence it's A

MathRevolution · Answer

Total number of ways:  ^3{C_1} * ^4{C_1} * ^6{C_1} * ^8{C_3}

=> 3 * 4 * 6 * 56

=> 4,032

Answer A

cherr012 · Answer

Total number of ways:  ^3{C_1} * ^4{C_1} * ^6{C_1} * ^8{C_3}

=> 3 * 4 * 6 * 56

=> 4,032

Here it is mentioned upto 3 which according to me means that the sandwich can have 0-3 choices of veggies , doesn't it?

Posted from my mobile device

Praveenksinha · Answer

Bunuel  I didn't get why A is correct. For veggies a person can choose up to 3 veggies, it can be 0,1,2 or 3. Please help why 8C3 is correct.

Bunuel · Answer

Anyone else wants to try?

yashikaaggarwal · Answer

Meat, Bread and Cheeses can be selected in 6C1*3C1*4C1 = 72 ways
Veggies portion is Optional.
Anyone can include veggies in their sandwiches up to 3 options out of 8

Let say there are 4 persons
=> A want sandwich with all 3 veggies kind
=> B want sandwich with 2 veggies kind
=> C want sandwich with only 1 veggie kind
=> D want sandwich with No Veggie

=> A can take sandwich in 8C3*72 = 4032 ways
=> B can take sandwich in 8C2*72 = 2016 ways
=> C can take sandwich in 8C1*72 = 576 ways
=> D can take sandwich in 8C0*72 = 72 ways (8C0 = 1)

Total ways = 4032+2016+576+72 = 6696 ways.

Answer is C

Posted from my mobile device

Neha2404 · Answer

IMO- C
In this question 
Choose of veggies is optional 
Customer can choose veggies in 4 ways 
No veggies- 3C1*6C1*4C1*8C0. =72
1 veggies - 3C1*6C1*4C1*8C1 =576
2 veggies- 3C1*6C1*4C1*8C2. =2016
3 veggies- 3C1*6C1*4C1*8C3. =4032
Total ways. To select a sandwich. =72+576+2016+4032
 =6696

Posted from my mobile device

navderm · Answer

Doing any calculation more than needed is a waste of time here.

We know that there are 3C1 ways of choosing the bread, 6C1 ways of choosing the meats, and 4C1 ways of choosing the cheese. 
So that makes 3 * 6 * 4 = 72

Now, we can choose 0, 1, 2, or 3 of the 8 vegetables.
That is (8C0 + 8C1 + 8C2 + 8C3) = 93

Since one of the aforementioned combinations of vegetables will always be chosen with the calculated combination of bread, meats, and cheese. 
it's 72 * 93

Looking at ones place of both those numbers, 2 * 3 = 6. Only C has 6 in it's unit place. 
So, C

tleknight · Answer

=   x  
= 72 x 93 
= 6696

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Rick’s Sandwich Shop lets customers create their own sandwiches by cho

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