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A certain gallery is hanging a series of 7 paintings. All th

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Director
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A certain gallery is hanging a series of 7 paintings. All th [#permalink] New post 30 Mar 2018, 01:09
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A certain gallery is hanging a series of 7 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 2 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?

A)240
B)200
C)122
D)80
E)16
[Reveal] Spoiler: OA
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Re: A certain gallery is hanging a series of 7 paintings. All th [#permalink] New post 31 Mar 2018, 20:50
this is the question of permutation.
we can solve it my multiplying factors method.
there are 7 positions for painting.
and the painting C1 C2 C3 C4 C5 P1 P2 (c represents canvas and P represents panel)
_ _ _ _ _ _ _
1 2 3 4 5 6 7

we start from the restriction: position 2 has two possibilities (P1 AND P2).
then position 6 has one possibility (either P1 or P2 depending upon which one is hung in position 2).
then position 1 has 5, position 3 has 4,position 4 has 3 position 5 has 2 and subsequently position 7 has 1 option.

so ans: 5*2*4*3*2*1*1=240 ans
Re: A certain gallery is hanging a series of 7 paintings. All th   [#permalink] 31 Mar 2018, 20:50
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