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How many distinguishable ways are there to write 9 as the sum of  1's, 2's  and 3's, where the order of the addends matters? For example, 3+2+1+2+1  and 1+3+2+2+1are two different ways.

 Oct 31, 2020
 #1
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I count 70 such permutations as follows:

 

(1233, 1323, 1332, 2133, 2331, 3123, 3132, 3213, 3231, 3312, 3321, 11223, 11232, 11322, 12123, 12132, 12213, 12231, 12312, 12321, 13122, 13212, 13221, 21123, 21132, 21213, 21231, 21312, 21321, 22113, 22131, 22311, 23112, 23121, 23211, 31122, 31212, 31221, 32112, 32121, 32211, 111123, 111132, 111213, 111231, 111312, 111321, 112113, 112131, 112311, 113112, 113121, 113211, 121113, 121131, 121311, 123111, 131112, 131121, 131211, 132111, 211113, 211131, 211311, 213111, 311112, 311121, 311211, 312111, 321111)=70 permutations.

 Oct 31, 2020

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