If you buy three pairs of jeans four sweaters and two pairs

If you buy three pairs of jeans, four sweaters, and two pairs of boots, how many new outfits (consisting of a new pair of jeans, a new sweater, and a new pair of boots) will you have? A certain model of automobile is available in six exterior colors, three interior colors, and three interior styles. In addition, the transmission can be either manual or automatic, and the engine can have either four or six cylinders. How many different versions of the automobile can be ordered? To fulfill requirements for a degree, a student must take one course each from the following groups: health, civics, critical thinking, and elective. If there are four health, three civics, six critical thinking, and

Solution

Number of exterior colors available = 6

Number of interior colors available = 3

Number of interior styles available = 3

Numer of transmission variants = 2

Numer of variants in engine = 2

Hence, total number of versions of automobile that can be = ⁶c₁ * ³c_{1 *}³c_{1 *}²c_{1 *} ²c_{1 *}

= 6 * 3 * 3 * 2 * 2

= 216