# The number of 6 digit numbers that can be formed using the digits 0,1,2,5,7 and 9 which are divisible by 11 and no digit is repeated, is: Option 1) 72 Option 2) 60 Option 3) 48 Option 4) 36

Sum of the given digit is 0+1+2+5+7+9 = 24

6 digit number let abcdef

abcdef is divisible by 11 if

$|(a+c+e)-(b+d+f)|$ is a multiple of 11

Only one possible is there

a+c+e=b+d+f=12

Case 1: {a,c,e}={7,5,0}

{b,d,f}={9,2,1}

So, 2 x 2! x 3! = 24

Case 2: {a,c,e}={9 , 2, 1}

{b,d,f}={7, 5, 0}

So, 3! x 3! = 36

Total = 24 + 36 = 60

So, correct option is (2).

Option 1)

72

Option 2)

60

Option 3)

48

Option 4)

36

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