The number of 9 digit numbers that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is \_\_
Answer: 60
Solutions · 1
Official solution
Digits of 123412341: 1,2,3,4,1,2,3,4,1 --- i.e. digit 1\times 3, 2\times 2, 3\times 2, 4\times 2.
Even digits present: 2 (\times 2), 4 (\times 2) --- 4 even digits total, to occupy the 4 even positions.
Arrangements of even digits (2,2,4,4) in 4 even places: 2!2!4!=6
Arrangements of odd digits (1,1,1,3,3) in 5 odd places: 3!2!5!=10
\[\text{Total} = 6\times10 = 60\]