Number of six digit numbers which have 3 digits even and 3 digits odd , if each digit is to be used atmost once is

Dear  student
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!
Regards