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AVprozaik [17]
3 years ago
6

This question is for only  the smart students

Mathematics
1 answer:
olga_2 [115]3 years ago
7 0
<span><span><span><span><span><span><span><span><span><span><span>5<span>a<span>−3</span></span></span><span>b2</span></span><span>(9)</span></span><span>a4</span></span><span>b6</span></span><span>(3)</span></span><span>a2</span></span><span>b3</span></span><span>(10)</span></span>a</span><span>b2</span></span><span>=<span><span><span>1350<span>a7</span></span><span>b13</span></span><span>a3</span></span></span><span>=<span><span>1350<span>a4</span></span><span>b<span>13</span></span></span></span>
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Answer:

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Explanation:

Number the sides of the decagon: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, from top (currently red) clockwise.

  • The side number one can be colored of five different colors (red, orange, blue, green, or yellow): 5
  • The side number two can be colored with four different colors: 4
  • The side number three can be colored with three different colors: 3
  • The side number four can be colored with two different colors: 2
  • The side number five can be colored with the only color left: 1
  • Each of the sides six through ten can be colored with one color, the same as its opposite side: 1

Thus, by the multiplication or fundamental principle of counting, the number of different ways to color the decagon will be:

  • 5 × 4 × 3 × 2 ×1 × 1 × 1 × 1 × 1 × 1 = 120.

Notice that numbering the sides starting from other than the top side is a rotation of the decagon, which would lead to identical coloring decagons, not adding a new way to the number of ways to color the sides of the figure.

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