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14 Oct 2021, 08:15
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
20% (01:48) correct
80%
(01:34)
wrong
based on 138
sessions
History
Date
Time
Result
Not Attempted Yet
An ice-cream sundae consists of two ice-cream scoops, one flavor per scoop, and one topping. How many different types of sundaes can be prepared if four ice-cream flavors and two toppings are available?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
14 Oct 2021, 18:51
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Bunuel
When answer choices are low in a Combinatorics question, I'll usually diagram out the options, as it's safer and spares me the trouble of worrying about which formula to use, what to divide it by, etc. In this case, I'd call the four ice-cream flavors A, B, C, and D and proceed to diagram the options for the two scoops as follows (noting that the problem doesn't explicitly require us to use two different flavors for the sundae):
AA
AB
AC
AD
BB
BC
BD
CC
CD
DD
So there are 10 possibilities for the flavors of the two scoops in the sundae. Now there are toppings to consider. For each of the 10 flavor combinations listed above, there are two options for toppings. This means that there are 10 scoop combinations with topping 1 and the same 10 scoop combinations with topping 2, for a total of 10 + 10 = 20 combinations. The correct answer is (E).
02 Nov 2024, 00:25
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Bunuel, can you help me understand what is wrong in doing: 4C2 * 2C1 (Chose 2 flavorus from 4 available and 1 topping from 2 available)
