8-digit numbers are formed using the digits 1, 1, 2, $2,2,3,4,4$. The number of such numbers in which the…
8-digit numbers are formed using the digits 1, 1, 2, $2,2,3,4,4$. The number of such numbers in which the odd digits do no occupy odd places, is:
160
120
60
48
Solution
In 8 digits numbers, 4 places are odd places.
Also, in the given 8 digits, there are three odd digits 1,1 and 3.
No. of ways three odd digits arranged at
$
\text { four even places }=\frac{4 P_3}{2 !}=\frac{4 !}{2 !}
$
No. of ways the remaining five digits 2 , 2, 2, 4 and 4 arranged at remaining five places $=\frac{5 !}{3 ! 2 !}$
Hence, required number of 8 digits number $=\frac{4 !}{2 !} \times \frac{5 !}{3 ! 2 !}=120$