Question

Number of six digit numbers which have $3$ digits even & $3$ digits odd, If each digit is to be used atmost once is

• A. $64800$
• B. $28600$
• C. $28800$
• D. $36000$

Answer 1

The correct option is A $64800$

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! = 64800