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# At a certain ice cream shop, a sundae contains two different scoops of

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Math Expert
Joined: 02 Sep 2009
Posts: 58421
At a certain ice cream shop, a sundae contains two different scoops of  [#permalink]

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27 Feb 2019, 23:11
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Difficulty:

25% (medium)

Question Stats:

63% (00:41) correct 37% (00:41) wrong based on 51 sessions

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At a certain ice cream shop, a sundae contains two different scoops of ice cream. If the shop sells 20 varieties of ice cream, how many different sundaes are possible?

A. 40
B. 190
C. 200
D. 380
E. 400

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At a certain ice cream shop, a sundae contains two different scoops of  [#permalink]

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Updated on: 28 Feb 2019, 22:53
Bunuel wrote:
At a certain ice cream shop, a sundae contains two different scoops of ice cream. If the shop sells 20 varieties of ice cream, how many different sundaes are possible?

A. 40
B. 190
C. 200
D. 380
E. 400

scoopes options

20C2 ; 190
IMO B

Originally posted by Archit3110 on 28 Feb 2019, 03:34.
Last edited by Archit3110 on 28 Feb 2019, 22:53, edited 1 time in total.
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Re: At a certain ice cream shop, a sundae contains two different scoops of  [#permalink]

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28 Feb 2019, 13:12
1
20C2 = 190, IMO Ans B

(Order is irrelevant here, hence, Ans cannot be D).

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Re: At a certain ice cream shop, a sundae contains two different scoops of  [#permalink]

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28 Feb 2019, 22:10
It can be solved using fundamental counting principle. The first scoop has 20 possibilities and the second has 19 (since different). But we need to eliminate duplicates in this because of ordering. Example: S1=Strawberry, S2=Chocolate or S1=Chocolate, S2=Strawberry are the same. 20*19/2=190. So answer choice B.
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Re: At a certain ice cream shop, a sundae contains two different scoops of  [#permalink]

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04 Mar 2019, 20:11
Bunuel wrote:
At a certain ice cream shop, a sundae contains two different scoops of ice cream. If the shop sells 20 varieties of ice cream, how many different sundaes are possible?

A. 40
B. 190
C. 200
D. 380
E. 400

The number of possible sundaes is 20C2 = 20!/(2! x 18!) = (20 x 19)/2! = 10 x 19 = 190.

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Re: At a certain ice cream shop, a sundae contains two different scoops of   [#permalink] 04 Mar 2019, 20:11
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