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How many five digit numbers can be formed using $2, 3, 8, 7, 5$ exactly once such that the number is divisible by $125$?

1. $0$
2. $1$
3. $4$
4. $4$

A number is divisible by 125, if its last three figures are zeros or a multiple of 125.

So,there are 2 possibilities i.e. 375 and and 875.

Case i :- last three figures is 375

If last three figures is 375 then there are 2 possibilities

28375

82375

Case ii :- last three figures is 875

If last three figures is 875 then there are 2 possibilities

23875

32875

There are only 4 possible numbers i.e. 28375 , 82375 , 23875 , 32875

Hence (C)and (D) is the Answer.