Discrete Mathematics A company produces 8 different sweater designs. Each sweater is made from three different pieces (top, middle, and bottom). There are six colors available and each piece in a sweater must have a different color. How many collections of 8 designs are possible if each color appears in at least one of the designs?
Unitary Method
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Discrete Mathematics
A company produces 8 different sweater designs. Each sweater is made from three different pieces (top, middle, and bottom). There are six colors available and each piece in a sweater must have a different color. How many collections of 8 designs are possible if each color appears in at least one of the designs?
Given that there are different types of sweater designs.
Each sweater is made from three different pieces. There are six colors and each piece in a sweater must have a different color this means that the piece in a sweater design have different color.
First consider two sweater design, each design has three different pieces and all have different colors.
If we color the top piece of first design with any one of six color then the middle piece of first design can be of any one color of the remaining colors.
The bottom piece of first design will of any color of the remaining colors. For second design there colors left
The top piece of second design can be any of the colors and the middle piece of second design can be of any two colors. The bottom piece of second design can be of the last color left
From this two designs,
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