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How many permutations of 3 different digits are there from the ten digits 0 to 9 inc?
The answer is 10P3 = 10!/(10-3)! = 10*9*8 = 720
How many four digit numbers can be formed from digits 1 2 3 4 if repeated is allowed and how many are odd numbers?
This is permutations with repetition. The answer is 4^4 = 256 total permutations. Since 2 of the digits used are odd (and 2 are even), then half of the possibilities will be odd: 128 odd numbers.
How many permutations can you get with 3 letters and 3 digits in the following format AAA000 - ZZZ999?
The answer is 26*26*26*10*10*10 = 17,576,000
How do you unlock 5 digits lock?
If you wish to use a brute-force method, assuming the digits go from 0 to 9 there are 10,000 possible permutations.
How many license plates can be made using three digits and three letters without repetition and alternating letters and digits?
If it alternates and you start with a letter, then there are 11,232,000 permutations. Then if you start with a number and alternate, there are another 11,232,000 permutations, for a total of 22,464,000 permutations. If you exclude the letters I, S, B, and O (because they look kind-of like 1, 5, 8, & 0 - kind-of important on license plates) then you are down to 6,652,800 & 13,305,600 respectively.
