Latest TCS Aptitude Question SOLUTION: What is the probability that a 9 digit number formed using 1,2,3,4,5,6,7,8,9 is divisible by 36.(without repetition)

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What is the probability that a 9 digit number formed using 1,2,3,4,5,6,7,8,9 is divisible by 36.(without repetition)

Asked In TCS ashokkumar (10 years ago)

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tejaswi chitta  (10 years ago)

ans: 2/9
here the 9digit number formed should be divisible by 36
36=9*4
ie the number should be divisible by both 9 nd 4
1+2+3+...+9 = 45
so every number formed with these digits can be divisible by 9
now the last two digits of the number should be divisible by 4
so last 2 digits can be 12,16,24,28,32,36,48,52,56,64,68,72,76,84,92,98
total 16 possibilities
so starting 7 digits can be arranged in 7! ways
so probability = (16 * 7!)/9!

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karthi keyan  (10 years ago)

@ROJA Probability is asked. Not the number of ways. Probability can never be greater than 1.

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roja  (10 years ago)

the num which is divisible 36 will always divisible by 9&4 which are co-primes. from the nums 1,2,3,4,5,6,7,8,9 the num divisble by both 9&4 will have last 2 digits as 72or54or36 and the remaining 7 places are arranged in 7! ways.so the ans is 3*7!

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Lakshmi.B  (10 years ago)

y it can't b 6*6 and divisibility rule for 3 and 2 can be checked and hence 8!*4/9! will b the ans.

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Guru Pranav  (10 years ago)

Nice question !!!

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Shweta  (5 years ago)

there are 9 places to fill. the last digit can be filled with the digits (2 or 4 or 6 or 8), so there are 4 ways and similarly the second last digit can be filled with (2 or 4 or 6 or 8), i.e that there are four ways.
and the remaining 7 digits can be filled in 7 ways (7!). therefore, 4*4*7!. in order to find the probability, we divide (4*4*7!) with 9! . THUS, THE ANSWER IS (4*4*7!)/9! i.e., 2/9.

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