pizza
There are 5 numbers of 1 digit, 25 numbers of 2 digits, and 75 numbers of 3 digits. This makes 105 numbers in all.
Allowing repetitions, there are 9 combinations. Without repeated digits, there is only one combination of 3 digits from 3.
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
2
27 three digit numbers from the digits 3, 5, 7 including repetitions.
24 three digit numbers if repetition of digits is not allowed. 4P3 = 24.If repetition of digits is allowed then we have:For 3 repetitions, 4 three digit numbers.For 2 repetitions, 36 three digit numbers.So we have a total of 64 three digit numbers if repetition of digits is allowed.
pizza
There are 5 numbers of 1 digit, 25 numbers of 2 digits, and 75 numbers of 3 digits. This makes 105 numbers in all.
There is no limitation given to the number of digits in the number, thus: For 3 digit numbers: to be less than 500 the first digit can be only one of {1, 2, 3, 4} leading to 4 × 5 × 4 = 80 numbers For 2 digit numbers: they are all less than 500, and there are 6 × 5 = 30 numbers For 1 digit numbers: they are all less than 500, and there are 6 numbers Thus there are in total 80 + 30 + 6 = 116 numbers that can be made form the digits {1, 2, 3, 4, 5 ,6} without repetitions that are less than 500.
2,401
It is possible to create a 3-digit number, without repeated digits so the probability is 1.
10,000
Allowing repetitions, there are 9 combinations. Without repeated digits, there is only one combination of 3 digits from 3.
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).
There are 7,290 different 4-digit numbers that can be formed from the digits 1-9 without repetition.
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