Questions & Answers

Question

Answers

$\left( a \right)\dfrac{7}{{275}}$

$\left( b \right)\dfrac{1}{{501}}$

$\left( c \right)\dfrac{1}{{504}}$

$\left( d \right)$ None of these

Answer
Verified

A three wheel combination lock.

Every wheel has digits from 1 to 9.

Now we have to find the probability of a person guessing the right combination if no digit is repeated.

As we know that the probability is the ratio of favorable number of outcomes to the total number of outcomes.

$ \Rightarrow P = \dfrac{{{\text{favorable number of outcomes}}}}{{{\text{total number of outcomes}}}}$

Know as we know that there is only 1 right three digit combination, so the favorable number of outcomes = 1.

Now find the total number of three digit combinations.

As there are 9 digits available so the first digit of a three digit combination is filled by 9 ways.

Now as one digit is exhausted and no digit is repeated so the number of ways to fill the second digit of a three digit combination is 8.

Similarly the number of ways to fill the third digit of a three digit combination is 7.

So the total number of three digit combinations is the multiplication of the above cases.

So the total number of three digit combinations = $9 \times 8 \times 7 = 504$

So the total number of outcomes is 504.

So the probability is, $P = \dfrac{1}{{504}}$.

So this is the required answer.