Question

How many 6 digit numbers can be formed from the digits 0,1,3,5,7and 9 which are divisibleby 10 and no digit is repeated?

Answer 1

many numbers can  be formed-

135790

315970

513790

751390

951370 etc.

make sure that the number ends with 0 the it is divisible by 10

Answer 2

For a number to be divisible by 10, its unit digit should be 0.
So we can arrange rest 5 numbers (1,3,5,7,9) in the five places without repeating.
It can be done in ⁵P₅ ways.

⁵P₅ = $\frac{5!}{(5-5)!} = \frac{5!}{0!}= \frac{120}{1} = 120$ numbers