P & C - 2 (SNAP-2008)

A number lock consists of 3 rings each marked with 10 different numbers. In how many cases the lock can not be opened

                          

(A)  3¹⁰        (B)  10³        (C) 30        (D) 999   (E) none

Solution follows here:

Solution:

To open the lock, we need to fix one number in each of the three rings. Given that each ring has 10 different numbers.

All possibilities for the first ring = 10

All possibilities for the second ring = 10

All possibilities for the third ring = 10

These three are independent activities.

From fundamental principle, all possibilities = 10 * 10 * 10 = 1000

But out of all these, only one possibility can open the lock and rest 999 possibilities can not open the lock.

Answer (D)