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avatar+15 

Find the number of positive integers that satisfy both the following conditions:

Each digit is a 1 or a 2

The sum of the digits is 8

 Sep 24, 2023
 #1
avatar-151 
-2

We can solve this problem using stars and bars. We have 8 stars, representing the digits of the number, and we need to divide them into 2 groups, representing the 2s and the 1s. We can do this in (2−18+2−1​)=36​ ways.

 Sep 25, 2023
 #2
avatar+128816 
+1

11111111 = 1  identifiable   integer

 

1111112 =    C(7,1)  = 7    identifiable integers

 

111122  =    C(6,2)   =   15  identifiable integers

 

11222 =  C (5,3)   =  10     identifiable integers

 

2222  = 1   identifiable integer

 

34  integers

 

cool cool cool

 Sep 27, 2023

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