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How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed?

How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed? Correct Answer 60

Calculation:

Numbers between 100 and 1000 are three digits number, so we have to fill three places.

Total numbers = 5

(They are 5, 6, 7, 8 and 9)

Number of choices for the 1st digit = 5

Repetition of digits is not allowed therefore available numbers for 2nd place is four

⇒ Number of choices for the 2nd digit = 4

Repetition of digits is not allowed therefore available numbers for 1st place is three

⇒ Number of choices for the 3rd digit = 3

∴ Total possible combinations = 5 × 4 × 3 = 60

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