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A person wants to form a four digit even number pin or three digit odd number pin using digits 0, 1, 2, ..., 9. How many such pins can be formed?

A person wants to form a four digit even number pin or three digit odd number pin using digits 0, 1, 2, ..., 9. How many such pins can be formed? Correct Answer 5500

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 four digit even number or three digit odd number using digits 0, 1, 2, ..., 9.

As we know that, a number is said to be even number if the unit digit is: 0, 2, 4, 6 or 8.

Number of ways to fill the units digit of a 4 digit even number pin = 5

Number of ways to fill the second digit of a 4 digit even number pin = 10

Number of ways to fill the third digit of a 4 digit even number pin = 10

Number of ways to fill the fourth digit of a 4 digit even number pin = 10

∴ Number of 4 digit even pin that can be generated = 5 × 10 × 10 × 10 = 5000

As we know that, a number is said to be odd if it is not divisible by 2 or in other words we can say that if the unit's digit is not occupied with 0, 2, 4, 6, 8.

Number of ways to fill the units digit of a 3 digit odd number pin = 5

Number of ways to fill the second digit of a 3 digit odd number pin = 10

Number of ways to fill the third digit of a 3 digit odd number pin = 10

∴ Number of 3 digit odd pin that can be generated = 5 × 10 × 10 = 500

∴ Number of 4 digit even pin or 3 digit odd pin that can be generated 5000 + 500 = 5500

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