Raial has 7 different posters to be hanged in her bedroom, living room and kitchen. Assuming she has plans to place at least a poster in each of the 3 rooms, how many choices does she have?

A.
49 
B.
170 
C.
21 
D.
210
Correct Answer: Option D
Explanation
The first poster has 7 ways to be arranges, the second poster can be arranged in 6 ways and the third poster in 5 ways.
= 7 x 6 x 5
= 210 ways
or (frac{7}{P_3}) = (frac{7!}{(7 – 3)!}) = (frac{7!}{4!})
= (frac{7 times 6 times 5 times 4!}{4!})
= 210 ways