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Bunuel
A restaurant menu features 5 appetizers, 6 entrées, and 3 desserts. If a dinner special consists of 1 appetizer, 1 entrée, and 1 dessert, how many different dinner specials are possible?

A. 30
B. 60
C. 90
D. 120
E. 150

Number of different dinners = 5C1 * 6C1 * 3C1 = 5*6*3 = 90

IMO C
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Five ways to select appetizer,six ways to select entrée, and 3 ways to select dessert,
Total: 5*6*3 = 90

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Bunuel
A restaurant menu features 5 appetizers, 6 entrées, and 3 desserts. If a dinner special consists of 1 appetizer, 1 entrée, and 1 dessert, how many different dinner specials are possible?

A. 30
B. 60
C. 90
D. 120
E. 150
total options
5c1*6c1*3c1; 90
IMO C
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This is a very easy question on Combinations. It’s also an apt question for anyone who’s starting off with the topic and wants to build a strong foundation, because solving such simple questions will give you a good idea of the fundamental concepts.

The number of ways of selecting ANY r objects out of the available n objects = \(n_c_r\) = \(\frac{n!}{(n-r)! * r!}\)

Since the dinner special has to contain ANY 1 appetizer, ANY 1 entree and ANY 1 dessert, we need to select the above from the available 5 appetizers, 6 entrees and 3 desserts.

No. of ways of selecting 1 appetizer out of 5 appetizers = \(5_C_1\) = 5. {\(n_c_1\) = n}

No. of ways of selecting 1 entrée out of 6 entrees = \(6_C_1\) = 6.

No. of ways of selecting 1 dessert out of 3 desserts = \(3_C_1\) = 3.

Therefore, number of ways of selecting 1 appetizer, 1 entrée AND 1 dessert = 5 * 6 * 3 = 90.
The correct answer option is C.

Hope this helps!
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Bunuel
A restaurant menu features 5 appetizers, 6 entrées, and 3 desserts. If a dinner special consists of 1 appetizer, 1 entrée, and 1 dessert, how many different dinner specials are possible?

A. 30
B. 60
C. 90
D. 120
E. 150


The number of possible dinner specials is 5 x 6 x 3 = 90.

Answer: C
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