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Division and Distributuion into Groups of Unequal Sizes.

A safety lock...

Question

A safety locker in a jewel shop requires a 4 digit unique code. The code has the digits from 0 to 9. How many unique codes are possible?

A

100

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B

1000

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C

10,000

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D

100,000

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Solution

The correct option is C 10,000
The unique code has 4 digits.

Each digit is formed using any of the 10 numbers from 0 to 9.
Hence, a single-digit number can be formed in 10 ways.

A double-digit number can be formed in 10 x 10 ways.

A three-digit number can be formed in 10 x 10 x 10 ways.

A four-digit number can be formed in 10 x 10 x 10 x 10 = 10,000 ways.

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