How many possible codes are there if the digits cannot be repeated? How many possible codes are there if the digits cannot be repeated? | Socratic (2024)

FAQs

How many possible codes are there if the digits cannot be repeated? How many possible codes are there if the digits cannot be repeated? | Socratic? ›

You have 10 different digits for the first place (that is, if 0 is allowed), when that is chosen, you have 9 left and so on, i.e. 10⋅9⋅8⋅7=5040 different codes.

examples. A 4 digit PIN number is selected. What is the probability that there are no repeated digits? There are 10 possible values for each digit of the PIN (namely: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9), so there are 10 · 10 · 10 · 10 = 10⁴ = 10000 total possible PIN numbers.

(n−r)! . How many 3-digit codes are possible if each digit is chosen from 0 through 9, and no digits are repeated. P(10,3)=10⋅9⋅8=720 . Hence, there are 720 possible 3-digit codes.

Thus, by multiplication principle, the required number of 4-digit numbers is 9×504=4536.

A : Total number of 4-digit codes = Each digit as 10 possibilities (0–9), so the count is 104=10000. 10 4 = 10000. Since you are asking about codes and not numbers so I'm assuming we are allowed to keep 0 at the ten thousands place. So unfavourable cases =1×1×1×10=10 = 1 × 1 × 1 × 10 = 10 cases.

When repetition is allowed, the number of possible permutations of 10 digits is 1010, or 10,000,000,000. When repetition is not allowed, the number of possible permutations of 10 digits is 10!, or 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800.

If what you want are all possible three digit numbers with no repetition of the digits then you have 10 choices for the first digit, you have 9 choices for the 2nd digit, and you have 8 choices for the 3rd digit giving you 10x9x8 = 720 in all.

Originally Answered: How many 4-digit combinations are possible using 0-9 without repeating any numbers? 5,040. If we were choosing any 4-digit number, we would have 10 choices for the first, 10 for the second, 10 for the third, and 10 for the fourth.

For example, there are five ways to combine four items from a set of five items. If one wants to know how many permutations of 4 items are there, they need only compute 4! = 4 x 3 x 2 x 1 = 24, i.e., there are 24 permutations of 4 items.

e.g. the numbers 1234 - can have up to 24 different combinations. some of them being 1234, 2341, 3412, 4123, etc.... up to 24 combinations. the numbers 1123 - can have up to 12 different combinations.

How long would it take to crack a 4 digit code? ›

If a password is only four or five characters (whether they are just numbers or a combination of numbers, letters and symbols), there's a very high chance that it will be hacked instantly. However, if a password is only numbers and up to 18 characters, it could take a hacker up to nine months to crack the code.