Question

Thomas is remodeling his living room. He is deciding on the options shown: Floor: Carpet, Hardwood, Tile Paint: Khaki, Green, Red, Blue Seating: Leather Sofa, Cloth Sofa Entertainment: LCD TV, Plasma TV If Thomas is choosing 1 from each of the categories shown, how many ways can Thomas remodel his living room?

Answer 1

Answer:

$48$

Step-by-step explanation:

GIVEN: Thomas is remodeling his living room. He is deciding on the options shown: Floor: Carpet, Hardwood, Tile Paint: Khaki, Green, Red, Blue Seating: Leather Sofa, Cloth Sofa Entertainment: LCD TV, Plasma TV.

TO FIND: If Thomas is choosing $1$ from each of the categories shown, how many ways can Thomas remodel his living room.

SOLUTION:

Total options for floor $=3$

number of ways of selecting floor $=^3C_1$

Total options for Paint $=4$

number of ways of selecting paint $^4C_1$

Total options for Seating $=2$

number of ways of selecting Seating $=^2C_1$

Total options for Entertainment $=2$

number of ways of selecting Entertainment $=^2C_1$

Total ways of selecting $1$ from each category $=^3C_1\times ^4C_1\times ^2C_1 \times ^2C_1$

                                                                          $=48$

Hence there are $48$ of remodeling living room.