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A person wants to create a four digit pin for his smart phone using the digits 0, 1, 2, ...9. How many different pins can he generate when repetition of digits is allowed? Note: 0 can be included at all places.

A person wants to create a four digit pin for his smart phone using the digits 0, 1, 2, ...9. How many different pins can he generate when repetition of digits is allowed? Note: 0 can be included at all places. Correct Answer 10,000

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 generate a 4-digit pin using digits 0, 1, 2,..,9.

Number of ways to fill the 1st - digit = 10

Number of ways to fill the 2nd - digit = 10

Number of ways to fill the 3rd-digit = 10

Number of ways to fill the 4th- digit = 10

∴ Number of ways to generate different 4 digit pin = 10× 10 × 10 × 10 = 10, 000 

 

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