Question

In how many ways can the digits of the number 2,2,3,3,5,5,8,8,8,8 be arranged so that the odd digits are placed in even positions?

Answer 1

even positions=5 so the nos can be placed in 5! ways and 3 is repeated twice and also 5 is repeated twice so... 5!/2!*2!=30

after 4 odd nos are placed then we have 6 positions for other nos to be placed so...same as 6!ways and 2 is repeated twice and 8 is repeated four times... 6!/2!*4!=15

so 30*15=450             ans

  OR

odd place combination = 5!/2!*2!=30

even place combination= 6!/2!*4!=15

to total=30*15=450                ans