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

`48`

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* ^4C_1* ^2C_1 * ^2C_1`

`=48`

Hence there are
`48` of remodeling living room.