No. of 6-digit nos. which have 3 digits even and 3-digits odd, if each digit is to be used at most once is?

Dear Jee king

number of ways of selection of 3  even number from 0,2,4,6,8  is  ⁵C₃

number of ways of selection of 3 odd number from 1,3,5,7,9  is  ⁵C₃

Total ways =⁵C₃⁵C₃ 6!

but this number also include zero at first place

  total number in which zero at place place = ⁵C₃⁴C₂ 5!

 

so total number  =⁵C₃⁵C₃ 6! -⁵C₃⁴C₂ 5!

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