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28 November, 17:08

1. Alicia has 7 paintings she wants to hang side by side on her wall.

(a) In how many ways can she arrange all 7 paintings? Show your work.

(b) If she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.

(c) In how many ways can she arrange 4 out of the 7 paintings? Show your work.

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  1. 28 November, 23:25
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    (a) Alicia can arrange all 7 paintings 5,040 ways.

    7! or 7*6*5*4*3*2*1

    (b) Alicia can choose the paintings she wishes to display in 35 ways, choosing 4 of the 7 paintings.

    7c4 or 7!/4! (7-4) ! or (7*6*5*4*3*2*1) / (4*3*2*1) (3*2*1)

    (c) Alicia can arrange 4 out of the 7 paintings in 840 ways.

    7p4 or 7! / (7-4) ! or (7*6*5*4*3*2*1) / (3*2*1)
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