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How much zeros has the number $1000!$ at the end? If a number ends with n n zeros than it is divisible by 10n 10 n, that is 2n5n 2 n 5 n A factorial clearly has more 2 2 s than 5 5 s in its factorization so you only need to count how many 5 5 s are there in the factorization of 1000! 1000!
statistics - If I ask $1000$ people to choose a random number between . . . Imagine I asked 1000 people to choose a number between 0 and 999 (both inclusive, the numbers are not biased, they will be completely random) and write that number down Now, after that, pick a number, x, where 0 ≤ x ≤ 1000 What is the probability that none of people that I asked will have chosen that number? I ran a simulation in Python to do this 10000 times (code), and in 37 22% of the
Find the number of times - Mathematics Stack Exchange Question: Find the number of times 5 5 will be written while listing integers from 1 1 to 1000 1000 Now, it can be solved in this fashion The numbers will be of the form: 5xy, x5y, xy5 5 x y, x 5 y, x y 5 where x, y x, y denote the two other digits such that 0 ≤ x, y ≤ 9 0 ≤ x, y ≤ 9 So, x, y x, y can take 10 10 choice each
Solution Verification: How many positive integers less than $1000$ have . . . A positive integer less than 1000 1000 has a unique representation as a 3 3 -digit number padded with leading zeros, if needed To avoid a digit of 9 9, you have 9 9 choices for each of the 3 3 digits, but you don't want all zeros, so the excluded set has count 93 − 1 = 728 9 3 − 1 = 728
algebra precalculus - Which is greater: $1000^ {1000}$ or $1001^ {999 . . . Question: Find the greater number: 10001000 or 1001999 My Attempt: I know that: (a + b)n ≥ an + an − 1bn Thus, (1 + 999)1000 ≥ 999001 And (1 + 1000)999 ≥ 999001 But that doesn't make much sense I want some hints regarding how to solve this problem Thanks
definition - What is the smallest binary number of $4$ bit? Is it . . . Problem: What is the smallest binary number of 4 4 bit? My approach: Today, my teacher asked me that and I replied (1000)2 (1000) 2 but my teacher said that it will be (0000)2 (0000) 2 If I ask someone what is the smallest decimal value of 2 2 digits, everyone will say 10 10 Will anyone say 00 00? Decimal and binary is the exact same thing except the "Digits Concept" (binary has 2 2 digits