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How many ways can a set of 3 not necessarily distinct numbers be chosen from the set of integers from 0 to 9? Two such sets are 5,2,4 and 0,0,7, but 2,4,5 is considered the same as 5,2,4

 Mar 27, 2020
 #1
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There should be: [10 +3 - 1] C 3 =12C3 = 220 ways

 

P.S. If you wanted a list of them, we can give you one.

 Mar 27, 2020
 #2
avatar+111330 
+1

Here is  how guest got that answer  :

 

If all the digits are differerent  we have C(10,3)  = 120  sets

 

If  two  digits  are the  same  and  the  other  is different,  we  hve 10 ways to pick the two digits and 9 ways to select the remaining one  = 10 * 9  =  90 sets

 

If all 3 digits are the same,  we have 10  sets

 

So

 

120  +  90  +  10   =    220  sets  (ways)

 

 

cool cool cool

 Mar 27, 2020

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