+0  
 
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 In how many ways can the digits of 45025 be arranged to form a 5-digit number?

 Jan 29, 2021
 #1
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+1

[(2, 0, 4, 5, 5), (2, 0, 5, 4, 5), (2, 0, 5, 5, 4), (2, 4, 0, 5, 5), (2, 4, 5, 0, 5), (2, 4, 5, 5, 0), (2, 5, 0, 4, 5), (2, 5, 0, 5, 4), (2, 5, 4, 0, 5), (2, 5, 4, 5, 0), (2, 5, 5, 0, 4), (2, 5, 5, 4, 0), (4, 0, 2, 5, 5), (4, 0, 5, 2, 5), (4, 0, 5, 5, 2), (4, 2, 0, 5, 5), (4, 2, 5, 0, 5), (4, 2, 5, 5, 0), (4, 5, 0, 2, 5), (4, 5, 0, 5, 2), (4, 5, 2, 0, 5), (4, 5, 2, 5, 0), (4, 5, 5, 0, 2), (4, 5, 5, 2, 0), (5, 0, 2, 4, 5), (5, 0, 2, 5, 4), (5, 0, 4, 2, 5), (5, 0, 4, 5, 2), (5, 0, 5, 2, 4), (5, 0, 5, 4, 2), (5, 2, 0, 4, 5), (5, 2, 0, 5, 4), (5, 2, 4, 0, 5), (5, 2, 4, 5, 0), (5, 2, 5, 0, 4), (5, 2, 5, 4, 0), (5, 4, 0, 2, 5), (5, 4, 0, 5, 2), (5, 4, 2, 0, 5), (5, 4, 2, 5, 0), (5, 4, 5, 0, 2), (5, 4, 5, 2, 0), (5, 5, 0, 2, 4), (5, 5, 0, 4, 2), (5, 5, 2, 0, 4), (5, 5, 2, 4, 0), (5, 5, 4, 0, 2), (5, 5, 4, 2, 0)] >Total distinct permutations = 48 ways.

 Jan 29, 2021
 #2
avatar+116126 
+1

Put the  0   in any  one of the trailing  four positions

 

And the  rest of the digits can be arranged in  4!/2!  identifiable ways  =   24/2 =  12  ways

 

So  4 * 12  =   48.....just as the guest found  !!!!

 

 

cool cool cool

 Jan 29, 2021

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