# Permutation problem 27 october

**Question**

How many !!5!! digit numbers divisible by !!5!! can be formed using !!0,1,2,3,4,5!! if repeatition not allowed.

!!a)" "220!!

!!b)" "240!!

!!c)" "!!None

**Solution**

Since repeatition not allowed so we can use a number only once.For number to be divisible by !!5!!, its unit place must have either !!0!! or !!5!!.

!!Case 1!!

Lets fix !!0!! at unit place the we can arrange rest digits in the form of !!5xx4xx3xx2 = 120!!

!!Case 2!!

Now if we will !!5!! at unit place, we can arrange rest numbers as !!4xx4xx3xx2 = 96!!

Hence total numbers !!= 120 + 96 = 216!!