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Q: How many four digit numbers can be formed from the digits 1 and 2 if repetitions are allowed?

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There are 5 numbers of 1 digit, 25 numbers of 2 digits, and 75 numbers of 3 digits. This makes 105 numbers in all.

Assuming all 45 digits are different (which they will not be if they are ordinary integers), then 456, if repetitions are allowed. That is 8303765625. If repetitions are not allowed then the number falls to 45*44*43*42*41*40 = 5864443200

504

64 if repetition is allowed.24 if repetition is not allowed.

If repetition of digits isn't allowed, then no13-digit sequencescan be formed from only 5 digits.

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There are 5 numbers of 1 digit, 25 numbers of 2 digits, and 75 numbers of 3 digits. This makes 105 numbers in all.

2,401

Assuming all 45 digits are different (which they will not be if they are ordinary integers), then 456, if repetitions are allowed. That is 8303765625. If repetitions are not allowed then the number falls to 45*44*43*42*41*40 = 5864443200

10,000

5^4

27 three digit numbers from the digits 3, 5, 7 including repetitions.

504

543210

64 if repetition is allowed.24 if repetition is not allowed.

The number of six digit numbers that you can make from ten different digits ifrepetitions of same digit on the six digit number is allowed is 1 000 000 numbers(including number 000 000).If no repetitions of the the same digit are allowed then you have:10P6 = 10!/(10-6)! = 151 200 different six digit numbers(six digit permutations form 10 different digits).

If repetition of digits isn't allowed, then no13-digit sequencescan be formed from only 5 digits.

125