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Robin chooses a 4-digit PIN number, so that there are exactly two different digits (like 0777). How many different PIN numbers can Robin choose?

 Mar 20, 2019
 #1
avatar+4779 
+1

\(\dbinom{4}{2} \dbinom{10}{2}+2\dbinom{4}{1}\dbinom{10}{2} = 630\)

 

The first term picks 2 slots from 4 in the code for the first digit and then picks 2 digits from 10 to use.

 

The second term picks 1 slot from the 4 to use for the first digit and then picks 2 digits from 10.

The factor of 2 is there because either digit can be the singleton, the other will be the triplet.

 Mar 20, 2019
 #2
avatar+17990 
+2

How many ways can you choose 2 digits out of 10?     10 C 2   = 45

IN 4 slots how many ways can you arrane these 2 digits?   2^4 = 16

   But two of these are without the second digit   (like 3333 and 4444) ....   so 16-2 = 14 ways

14 x 45 = 630 combos.

 Mar 20, 2019

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