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i am not underage, i'm just inept at probability
we have a pin code made up of 4 *distinct* numbers, guessing the first digit has a probability of 1/10, guessing the next should have a probability of 1/9 and so on (because the numbers are distinct), therefore the probability of someone guessing the code by inputting random digits is 1/(10*9*8*7), is this correct?
moreover the probability of someone guessing all digits but not necessarily in the correct position should be the previous probability multiplied by 4! because that's all the possible combinations of the digits one can try, correct?
finally someone guessing at least 2 numbers in the correct position should be (1/(10*9) * (1/8*7)*2!) because it's the probability of guessing 2 digits in 2 correct positions * all possible combinations of the remaining digits, is this correct?
we have a pin code made up of 4 *distinct* numbers, guessing the first digit has a probability of 1/10, guessing the next should have a probability of 1/9 and so on (because the numbers are distinct), therefore the probability of someone guessing the code by inputting random digits is 1/(10*9*8*7), is this correct?
moreover the probability of someone guessing all digits but not necessarily in the correct position should be the previous probability multiplied by 4! because that's all the possible combinations of the digits one can try, correct?
finally someone guessing at least 2 numbers in the correct position should be (1/(10*9) * (1/8*7)*2!) because it's the probability of guessing 2 digits in 2 correct positions * all possible combinations of the remaining digits, is this correct?
