Correct Answer - Option 1 : 60
Concept:
Fundamental principal of multiplication:
Let us suppose there are two tasks A and B such that the task A can be done in m different ways following which the second task B can be done in n different ways. Then the number of ways to complete the task A and B in succession respectively is given by: m × n ways
Fundamental principal of addition:
Let us suppose there are two tasks A and B such that the task A can be done in m different ways and task B can be completed in n ways. Then the number of ways to complete either of the two tasks is given by: (m + n) ways.
Calculation:
Here we have to form 3 digit numbers without using the digits 0, 1, 4, 5, 7 such that repetition of digits is not allowed.
The hundredth digit can be filled by any digit except 0, 1, 4, 5, 7
⇒ No. of ways to fill hundredth digit = 5
No. of ways to fill tenth digit = 4
No. of ways to fill unit’s digit = 3
So, number of 3 digit numbers which can be formed = 5 × 4 × 3 = 60
