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The positive five-digit integers that use each of the digits 1, 2, 3, 4 and 5 exactly once are ordered from least to greatest. What is the 50th integer in the list?

 

thank you to whoever helps!

:)

 Apr 23, 2020
 #1
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+2

Hi Loki,

 

Lets say the first digit is 1

it will be followed by 2,3,4,5     there will be 4! = 24 ways that these number can be arranged so that accounts for the smallest 24 numbers

If the first number is 2 followed by the others then again this will account for another 24 numbers.

 

so

25431 is the 48th number

31245 is the 49th

31254 is the 50th.

 

The question is not well worded but I think that is what is meant.

 Apr 23, 2020
 #2
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+2

Right on the money!:

 

12345 , 12354 , 12435 , 12453 , 12534 , 12543 , 13245 , 13254 , 13425 , 13452 , 13524 , 13542 , 14235 , 14253 , 14325 , 14352 , 14523 , 14532 , 15234 , 15243 , 15324 , 15342 , 15423 , 15432 , 21345 , 21354 , 21435 , 21453 , 21534 , 21543 , 23145 , 23154 , 23415 , 23451 , 23514 , 23541 , 24135 , 24153 , 24315 , 24351 , 24513 , 24531 , 25134 , 25143 , 25314 , 25341 , 25413 , 25431 , 31245 , 31254 (50th number).

Guest Apr 23, 2020

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