6) A garden is 90m long and 50m wide. A path of 5m width is built outside and around it.
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2734375 employee ID codes can be generated
<em><u>Solution:</u></em>
Given that Each code will have one digit followed by four letters
The letter V and the digits 3, 4, and 5 will not be used
So, there are 25 letters and 7 digits that will be used
Assume that the letters can be repeated
Each code = 1 digit + four letters
digits 3 , 4 , 5 cannot be used
Therefore, the remaining digits are 1, 2, 6, 7, 8 , 9, 0
7 digits that will be used
One digit can be chosen from 7 digits in 7 ways
The first letter can be chosen from 25 letters in 25 ways
Since given that letters can be repeated
The second letter can be chosen from 25 letters in 25 ways
Similarly, the third letter can be chosen from 25 letters in 25 ways
Similarly, the fourth letter can be chosen from 25 letters in 25 ways
<u><em>Therefore, the total number of ways are:</em></u>
Thus 2734375 employee ID codes can be generated