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A 5 digit no. formed by usng 0,1,2,3,4,5 without repitition the prob. that it is divisible by 6 ?
Dear Mayank
a number is divisibe by 3 and 2 then it is divisible by 6
divisibility by 2
digit at unit place must be even
divisibility by 3
sum of the digit divisible by 3
so only two combination is possible 1,2,3,4,5 and 0,1,2,4,5
for 1,2,3,4,5
unit place can be filled by 2 ways
all other 4 places can be filled by 4*3*2*1 ways
so total ways = 2*4*3*2*1 = 48 ways
for 0,1,2,4,5
0 is at unit place
all other 4 places can be filled by 4*3*2*1 ways = 24
0 is not at the unit place
all other place can be filled 3*3*2*1
total ways =2* 3*3*2*1 =36
so 48+ 24+36 = 108 ways
probability = 108/5*5*4*3*2
=.18
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