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How many different positive three-digit integers can be formed using only the digits in the set {2, 3, 5, 5, 5, 6, 6, 6} if no digit may be used more times than it appears in the given set of available digits?

 May 27, 2022
 #1
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+1

235 ( 6 ) , 236 ( 6 ) , 255 ( 3 ) , 256 ( 6 ) , 266 ( 3 ) , 355 ( 3 ) , 356 ( 6 ) , 366 ( 3 ) , 555 ( 1 ) , 556 ( 3 ) , 566 ( 3 ) , 666 ( 1 ) , >>Total combinations = 12


>>Totals in parentheses = 44 permutations.

 May 27, 2022
 #2
avatar+118146 
+1

 {2, 3, 5, 5, 5, 6, 6, 6}

all the same   

666       1

555        1

 

2 the same

665       3

663        3

662        3

556        3

553        3

552       3

 

All different

235         3!=6

236         3!=6

356         3!=6

 

2+18+18 = 38

 May 28, 2022
 #3
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0

Hi Melody: Did you miss 256 ==6 in the last category "All different" ?

Guest May 28, 2022
 #4
avatar+118146 
0

Zep. looks like I did so i better add 6.  That makes   44  And now we agree.

Thanks guest  :))

Melody  May 29, 2022

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