Seldon Ross

Question

How many 5 digit numbers can be formed from the integers 1,2......9 if no digit can appear more than twice?

Comments

how will you get four 1s??9 numbers each of two are there

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see now..

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From a set of 9 numbers each twice in number how you can get 4 1`s?

Answer 1

There will be three cases  :

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Case 1:  All numbers are different i.e 9c5 and then arrange them 5 ! so it would be :
               (9^c5) * 5! = 15120
Case 2 : One number is repeating and other are different something like 11234:

               (9^c1)*(8^c3) * 5!/2!   = 9!/3!*2! = 30240
Case 3 : two numbers are repeating and only one is diff something like 11223 :

               (9^c2)*(7^c1) * 5!/2!*2!   = 9*8*7*5!/2!2!2! = 7560

Total :   15120+30240+7560= 52920