SOLUTION: How many 6 digit Even numbers can be formed by using 1,2,2,4,4,4?

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Question 1108154: How many 6 digit Even numbers can be formed by using 1,2,2,4,4,4?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
In such numbers, the digit "1" can occupy any position, except the "ones" position.


There are    different even numbers, comprising of given digits and having "1" in the most-left position.


      (   is the number of distinguishable arrangements of the digits 2,2,4,4,4 )


There are    different even numbers, comprising of given digits and having "1" in the 2-nd position from the left.


    . . . .  and so on . . . 


There are    different even numbers, comprising of given digits and having "2" in the 5-nd position from the left.


In this way, you get all possible distinguishable arrangements, and their total number is   =  = 5*10 = 50 numbers.

------------
See the lesson
    - Arranging elements of sets containing indistinguishable elements
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



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