Problem Solving

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

pkw209 wrote: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

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P P


5 canvas can be arranged in 5! ways
2 panels in 2! ways

therefore 5!x2! = 240 ways.

becuase order matters we can just multiply the possibilities for each space.

First space has 5 choices, 2nd has 2, third has 4, 4th has 3, 5th has 2 6th has 1 and 7th has 1 so..

5*2*4*3*2*1*1=240

if you were simply grouping them it would be helpful to separate the groups but here it is not necessary.