Question
How many different numbers of 5-digit can be formed by using the digits 2,3, 4, 5 and 7, without repetition, so that the number is not divisible by 5?
Solution
Number of digit available = 5 (all distinct)
Number of digits to be used = 5
Since the number is not divisible by 5.
5 cannot occupy box 5.
Number of permutations for box 
...(i)
Now, we have 4-digits and 4 boxes.
Number of permutations = 
... (ii)
From (i) and (ii), the total number of permutations = 4 x 24 = 96
Hence, the number of numbers formed, that are not divisible by 5 = 96.
