Counting_Methods3(1&amp;2)

# Counting_Methods3(1&amp;amp;2) - the box? Counting methods...

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Counting methods 3 Three towns A, B and C are connected by a number of roads. There are three from A to B and two from B to C B A C

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Counting methods 3 A B C 2 ways A B C 2 ways A B C 2 ways
Counting methods 3 There are 6 ways of going from A to B to C i.e. 3 × 2 = 6 ways of making the trip A B C 2 ways A B C 2 ways A B C 2 ways

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Counting methods 3 Position 1 Position 2 Position 3 How many ways can 3 balls be placed in a row? FACTORIAL
Counting methods 3 With blue in the first position With red in the first position With green in the first position

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Counting methods 3 The number of ways = 3 × 2 × 1 = 6 ways If 4 balls were to be placed in a row the total number of ways would be 4 × 3 × 2 × 1 = 24 ways Note 3! = 3 × 2 × 1 4! = 4 × 3 × 2 × 1
Counting methods 3 6 4 2 5 3 1 How many ways can 4 rabbits be selected from

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Unformatted text preview: the box? Counting methods 3 Order does not matter and so all of the following are considered to be the same 2 3 1 3 2 2 2 3 3 3 3 2 2 1 1 1 1 1 Counting methods 3 Position 1 Position 2 Position 3 The first position can be filled in 6 ways, the second in 5 and the third in 4 ways. Thus there are 6 5 4 ways of placing the rabbits in a row of three But there are 3 2 1 ways of arranging a particular three rabbits in a row. Therefore the number of ways the rabbits can be chosen = 20 1 2 3 4 5 6 = Counting methods 3 123 124 125 126 134 135 136 145 146 156 234 235 236 245 246 256 345 346 356 456 The possible selections are as shown...
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## Counting_Methods3(1&amp;amp;2) - the box? Counting methods...

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