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A certain gallery is hanging a series

This topic has 1 expert reply and 0 member replies

A certain gallery is hanging a series

Post Fri Dec 15, 2017 7:18 am
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

The OA is A.

What is the formula that I should use to get the answer? I tried to solve it but I couldn't. Experts, I need your help. Thanks.

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Post Fri Dec 15, 2017 8:02 am
VJesus12 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

The OA is A.

What is the formula that I should use to get the answer? I tried to solve it but I couldn't. Experts, I need your help. Thanks.
If there are two paintings on panel, and there are two spots were we can place them, then there are 2! = 2 ways we can place those paintings.

If there are five paintings on canvas, and there are 5 remaining spots where these paintings can be placed, there are 5! = 120 ways we can place those paintings.

2*120 = 240. The answer is A

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