# Find the number of 4 digit numbers that can be formed using the digits 0, 1, 2, 4, 5, 7 such that if repetition of digits is not allowed.

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Find the number of 4 digit numbers that can be formed using the digits 0, 1, 2, 4, 5, 7 such that if repetition of digits is not allowed.
1. 360
2. 300
3. 60
4. 24

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Correct Answer - Option 2 : 300

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, 2, 4, 5, 7 such that repetition of digits is not allowed.

The hundredth digit can be filled by any digit except  0, 1, 2, 4, 5, 7

⇒ No.of ways to fills one thousand digit = 5

⇒ 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, the number of 4 digit numbers which can be formed = 5 × 5 × 4 × 3 = 300