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# Combinatorics Problem

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532
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+119

How many numbers (up to a maximum of four digit numbers) can be made from the digits 2, 3, 4, and 5 if no digit can be repeated?

I don't think I've gone over this yet in my course's material so I really have no clue how to even start answering this problem. Any help would be appreciated, as always...

Feb 15, 2018
edited by Aleguan  Feb 15, 2018

#1
+111329
+2

1 dgit numbers  = 4

2 digit numbers  = take any 2 of 4 numbers and permute them  =  P(4,2)  = 12

3 digit numbers  =   take any 3 of  4 numbers and permute them = P(4,3)   = 24

4 digit numbers  = permute all 4 numbers =  4!  =  24

So.....

4  + 12  +  2(24)    =     64 numbers

Feb 15, 2018
#2
+1

1- permutations{(2,3,4,5), 1}

{2} | {3} | {4} | {5} (total: 4)

2 -permutations{(2,3,4,5), 2}

{2, 3} | {2, 4} | {2, 5} | {3, 2} | {3, 4} | {3, 5} | {4, 2} | {4, 3} | {4, 5} | {5, 2} | {5, 3} | {5, 4} (total: 12)

3-permutations{(2,3,4,5), 3}

{2, 3, 4} | {2, 3, 5} | {2, 4, 3} | {2, 4, 5} | {2, 5, 3} | {2, 5, 4} | {3, 2, 4} | {3, 2, 5} | {3, 4, 2} | {3, 4, 5} | {3, 5, 2} | {3, 5, 4} | {4, 2, 3} | {4, 2, 5} | {4, 3, 2} | {4, 3, 5} | {4, 5, 2} | {4, 5, 3} | {5, 2, 3} | {5, 2, 4} | {5, 3, 2} | {5, 3, 4} | {5, 4, 2} | {5, 4, 3} (total: 24)

4-permutations{(2,3,4,5), 4}

{2, 3, 4, 5} | {2, 3, 5, 4} | {2, 4, 3, 5} | {2, 4, 5, 3} | {2, 5, 3, 4} | {2, 5, 4, 3} | {3, 2, 4, 5} | {3, 2, 5, 4} | {3, 4, 2, 5} | {3, 4, 5, 2} | {3, 5, 2, 4} | {3, 5, 4, 2} | {4, 2, 3, 5} | {4, 2, 5, 3} | {4, 3, 2, 5} | {4, 3, 5, 2} | {4, 5, 2, 3} | {4, 5, 3, 2} | {5, 2, 3, 4} | {5, 2, 4, 3} | {5, 3, 2, 4} | {5, 3, 4, 2} | {5, 4, 2, 3} | {5, 4, 3, 2} (total: 24)

Total =4 + 12 + 24 + 24 = 64 - permutations.

Feb 15, 2018