Question

A witness to a hit-and-run accident told the police that the license number contained the letters RLH followed by 3 digits, the first of which was a 5. If the witness cannot recall the last 2 digits, but is certain that all 3 digits are different, find the maximum number of automobile registrations that the police may have to check.

Answer 1

Answer:

72 license

Step-by-step explanation:

License no contains 6 digit of which 4 are already known RLH5_ _

Last two digit may any no from 0 to 9 except 5

So the no of ways = 9 × 8 = 72

2nd digit have 9 choices and first digit have 8 choice

Answer 2

Concept Introduction:-

Mathematics defines time as an ongoing and continuous series of events that take place in order, from the past to the present to the future.

Given Information:-

We have been given that a witness to a hit-and-run accident told the police that the license number contained the letters RLH followed by $3$ digits, the first of which was a $5$. If the witness cannot recall the last $2$ digits, but is certain that all $3$ digits are different.

To Find:-

We have to find that the maximum number of automobile registrations that the police may have to check.

Solution:-

According to the problem

Since digits are different, available digits are $0,1,2,3,4,6,7,8,9$ ( as $5$ is already used)

Number of available digits $= 9$

$2$nd digit can be any of the above $9$ digits

$3$rd digit can be any of the remaining $8$ digits

Police have to check $9 \times 8=72$ registrations.

Final Answer:-

The maximum number of automobile registrations that the police may have to check is $72$ license.