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Bunuel
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A principal has four different trophies available for display in his 06 Mar 2019, 23:58
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35% (medium)

Question Stats:

64% (00:51) correct 36% (00:56) wrong based on 268 sessions

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A principal has four different trophies available for display in his two display cases. If only one trophy can fit in each display case, how many distinct ways are there to display two of the trophies in the cases at any given time?

A. 16

B. 12

C. 9

D. 8

E. 6
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B
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A principal has four different trophies available for display in his 07 Mar 2019, 05:12
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Bunuel
A principal has four different trophies available for display in his two display cases. If only one trophy can fit in each display case, how many distinct ways are there to display two of the trophies in the cases at any given time?

A. 16

B. 12

C. 9

D. 8

E. 6
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4C2 * 2 = 6*2 = 12
IMO B
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A principal has four different trophies available for display in his 07 Mar 2019, 05:36
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For the first display 4 possible options.
And after one trophy is selected for the first display, the second can be selected in 3 possible ways(for 3 trophies)
4*3 = 12 possible ways

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A principal has four different trophies available for display in his 08 Oct 2020, 09:03
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The question is just asking us to find how many combinations are possible to select 2 items out of 4 items.
So shouldnt the answer just be 4C2? Why are we multiplying 2 to that again?

But if I apply FCP rule, I can understand it should 4 x 3 (=12)

Can someone please clarify this doubt? This is confusing me a lot of combinations problems
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A principal has four different trophies available for display in his 09 Oct 2020, 23:17
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The question says there are 2 display cases and there are 4 trophies

Now, let's take the 1st display case.

In the 1st case, the principal can place any of the 4 trophies. So, he keeps one of them there, ie, 4C1 = 4

Now, he has 3 trophies left with him and he can place any of the 3 trophies in the second display case. ie, 3C1 = 3

Now, we have to multiply them. 4C1 * 3C1 = 4*3 = 12

Answer B
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A principal has four different trophies available for display in his 10 Oct 2020, 10:50
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For first display we have '4' trophies and for second display we will have '3' trophies = 4 * 3 = 12

Answer B
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A principal has four different trophies available for display in his 29 Jan 2026, 07:40
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Deconstructing the Question

This is a Permutation problem because we are placing distinct items into distinct slots (display cases). The arrangement matters (Trophy A in Case 1 is different from Trophy A in Case 2).

Method: The Slot Approach
We have 2 empty spots (display cases) to fill using 4 distinct trophies.

  • Display Case 1: We can choose any of the 4 trophies.
  • Display Case 2: Since one trophy is already placed, we have 3 remaining options.

Calculation
Multiply the options for each independent slot:
\(Total Ways = 4 * 3 = \) 12

(Note: If the order didn't matter, the answer would be \(4C2 = 6\), which is answer E, but "display" implies arrangement).

The correct answer is B.
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