Question

A child attempts to open a five disc-lock (each disc consists of digits {0, 1, .... 9}) He takes 5 sec time to dial a particular number on the disc. If he does so for 5 hrs. every day, then the number of ways he would be sure to open the lock

• A. 300
• B. 280
• C. 278
• D. 250

Answer 1

Answer: (C)

278

Each disc contains the digits 0, 1, 2...9
Total no. of ways of dialing $={10}^5$
Time taken to dial each disc $=$ 5 sec $=$
$\frac{5}{60\times 60}hrs$
Assuming worst case situation where the last trial is the correct trial to get maximum possible time
.$\cdot$. Total time taken $=\frac{{10}^5\times 5}{60\times 60}hrs$
At the rate of 5 hrs of trial per 1 day
$\frac{{10}^5\times 5}{60\times 60\times 5}$ days $=277.77$ days
Therefore, the lock is opened on the 278th day