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How many ways can you go up a 10 step staircase if you have very long legs and make 1, 2, OR 3 step moves?

 Jul 7, 2018
 #1
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use case work

 Jul 7, 2018
 #2
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How many ways can you go up a 10 step staircase if you have very long legs and make 1, 2, OR 3 step moves?''

 

Lets see

3 3 3 1                 4 permutations

3 3 2 2                4!/(2!2!) 6 permutations 

3 3 2 1 1             5!/(2!2!) = 30 permutatiions

3 3 1 1 1 1          6!/(2!4!) = 15 permutations

3 2 2 2 1             5!/(3!) = 20 permutations

3 2 2 1 1 1          6!/(2!3!) = 60 permutations

3 2 1 1 1 1 1       7!/(5!) = 42 permutations

3 1 1 1 1 1 1 1     8!/7! = 8 permutations

2 2 2 2 2              1 permutation

2 2 2 2 1 1            6!/(4!2!) = 15 permutations

2 2 2 1 1 1 1          7!/(3!4!)= 35 permutations

2 2 1 1 1 1 1 1        8!/(2!6!)= 28 permutations

2 1 1 1 1 1 1 1 1      9!/(8!) = 9 permutations

1 1 1 1 1 1 1 1 1 1      1 permutation

 

4+6+30+15+20+60+42+8+1+15+35+28+9+1 = 274

 

I get 274   laugh

 Jul 7, 2018

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