Question

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.
Answer:

Answer 1

(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)