Question

How many ways can digits be arranged so that no even digit is in correct position

Answer 1

There are total 10 digits. These digits are

0 , 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 9 . These are written in correct order.

E, O, E,O ,E ,O , E,O,E, O

For no even digit to be in correct place, we can write these as

O, ....... , O, ......., O , ........, O, ........., O,........

First we can arrange 5 odd numbers in ways = 5! = 120 ways

And we can fill the blanks with Even numbers in ways = 5! = 120 ways

Mixing up both the arrangements, we have

Total ways = 120 × 120 = 14,400

Example:

one example is

1, ,0, 3, 2, 5, 4, 7, 6, 9, 8

In this example, no even digit is in correct order.