The 7 rooms of a new home are to be painted. Each room is to be painted one color from a selection of 4 shades of blue (B1,B2,B3,B4) and 3 shades of green (G1,G2,G3) and 2 shades of red (R1,R2). More than one room may have the same color.
Count the number of ways each of the following steps can be completed to determine the number of different ways to paint the 7 rooms.
a.) If 5 are to be painted a shade of blue and 2 a shade of green.
b.) 3 rooms some shade of red, 3 rooms some shade of blue and one room some shade of green, how many different ways can the seven rooms be painted?
c.)How many ways can the rooms be painted?
d.) How many different ways can all the rooms be painted red?
e.) How many different ways can the rooms be painted if atleast one room is green or blue?
Any help would be tremendously appreciated!!!