Question

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 ______.

Options

• 160

• 120

• 60

• 48

Answer 1

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 120.

Explanation:

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 four even places = `(""^4"P"_3)/(2!)` = `(4!)/(2!)`

No. of ways the remaining five digits 2, 2, 2, 4 and 4 arranged at remaining five places = `(5!)/(3!2!)`

Hence, required number of 8 digits number

= `(4!)/(2!) xx (5!)/(3!2!)`

= 120