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Rick’s Sandwich Shop lets customers create their own sandwic
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13 Aug 2020, 02:04
13 Aug 2020, 02:04
4
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Question Stats:
27% (02:36) correct
72% (02:01) wrong based on 160 sessions
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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
KUDOS for the right solution and explanation
A. 4,032
B. 6,624
C. 6,696
D. 24,192
E. 28,932
KUDOS for the right solution and explanation
Re: Rick’s Sandwich Shop lets customers create their own sandwic
[#permalink]
13 Aug 2020, 16:13
13 Aug 2020, 16:13
9
We can choose
1 out of 3 breads
1 out of 6 meats
1 out of 4 cheese
and we can choose 0,1,2, or 3 veggies out 8
Using Principle of Counting
Case1: Number of sandwiches when we choose no veggies
3*6*4= 72
Case2: Number of sandwiches when we choose 1 out of 8 veggies
3*6*4*8= 576
Case3: Number of sandwiches when we choose 2 out of 8 veggies
3*6*4*(8 choose 2)= 2016
Case4: Number of sandwiches when we choose 3 out of 8 veggies
3*6*4*(8 choose 3)= 4.032
Total Number of Sandwiches is: 72+576+504+4032 = 6696
Final Answer: C
1 out of 3 breads
1 out of 6 meats
1 out of 4 cheese
and we can choose 0,1,2, or 3 veggies out 8
Using Principle of Counting
Case1: Number of sandwiches when we choose no veggies
3*6*4= 72
Case2: Number of sandwiches when we choose 1 out of 8 veggies
3*6*4*8= 576
Case3: Number of sandwiches when we choose 2 out of 8 veggies
3*6*4*(8 choose 2)= 2016
Case4: Number of sandwiches when we choose 3 out of 8 veggies
3*6*4*(8 choose 3)= 4.032
Total Number of Sandwiches is: 72+576+504+4032 = 6696
Final Answer: C
General Discussion
Re: Ricks Sandwich Shop lets customers create their own sandwic
[#permalink]
12 Apr 2023, 06:55
12 Apr 2023, 06:55
1
Total = 3*6*4 + 3*6*4(8c0 + 8c1 + 8c2 + 8c3) = 6696
