Seven-thRow

Probability Level 3

A three digit number is formed by throwing a fair dice three times. If m out of n times the number so obtained is divisible by 7, then m + n equals: (m and n are relatively prime)

The answer is 41.

2 solutions

Brandon Xia
Mar 24, 2014

There are 216 possible numbers formed, and through some math, and or program, it turns out that 30 of those are divisible by 7. 30/216 = 5/36, 5+36 =41.

can u please explain the method , I got 216 as the possible numbers formed but what to do next?

Faisal Maniar - 7 years, 2 months ago

look at my solution below

Ghanashyam Chakravarthi - 7 years, 2 months ago

Ghanashyam Chakravarthi
Apr 9, 2014

There are $216$ total possibilities. Then we must find all numbers from $100-666$ that are divisible by $7$ and contain digits $1-6$ only, which turn out to be $30$ . { $161,231,441,511,651$ and so on,note that when u fix the last digit, the other two digits will be a part of an AP, so you can calculate easily.}

Thus the required probability is $\frac {30}{216} = \frac {5}{36}$ and the required answer is $5 + 36 = \boxed{41}$

Seven-thRow

The answer is 41.

2 solutions

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