Question 1135810
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There are two kinds of 6-digit numbers that contain only digits 1, 2, 3, and 4 with each of those digits occurring at least once:<br>
(1) 3 of one of the digits and 1 each of the other three<br>
You can choose any one of the 4 digits to be the one that is used 3 times: {{{C(4,1) = 4}}}
The number of different arrangements of the 6 digits is {{{6!/((3!)(1!)(1!)(1!)) =  120}}}<br>
Total number of 6-digit numbers of this type: 4*120 = 480<br>
(2) 2 each of 2 of the digits and 1 each of the other two<br>
You can choose any 2 of the 4 digits to be the ones that are used twice: {{{C(4,2) = 6}}}
The number of different arrangements of the 6 digits is{{{6!/((2!)(2!)(1!)(1!)) = 180}}}<br>
Total number of 6-digit numbers of this type: 6*180 = 1080<br>
Total number of 6-digit numbers that contain only digits 1, 2, 3, 4 with each being used at least once: 480+1080 = 1560