how many positive integers less than 1000 are there which contain one 4 or at least one 9 (or both)
There are numbers
that contain neither 4 nor 9. (The −1 is because 000
doesn't count).
Subtract that from the total number of integers less than 1000
Of course, since 0 doesn't have a 4 or 9 anyway, you could equally well ask about non-negative integers less than 1000, in which case you'd just subtract 83 from 103, getting the same result.
how many positive integers less than 1000 are there which contain one 4 or at least...
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using the inclusion-exclusion principle 3. For the purpose of this problem, a word is an ordered string of 5 lowercase letters from the English alphabet (i.e., the 26 letters from a to z). For example, "alpha" and "zfaxr" are words. A subword of a word is an ordered string that appears as consecutive letters anywhere within the given word. For example, "cat" is...
Question 1 (a) How many positive integers are there between 1000 and 4999, inclusive? (b) How many positive integers between 1000 and 4999, inclusive: 1. have no repeated digit? 2. have at least one repeated digit? 3. have at most two repeated digits? Note that by 'one repeated digit' we mean that there is a digit that appears at least twice (eg, 1123 has one repeated digit). Similarly, by two repeated digits we mean a digit that appears at least...
how many integers from 0 through 999,999 contain the digit 4 exactly twice? how many integers from 1 through 1000000 contain the digits 6 at least once
How many 6 digit positive integers are there that contain exactly 3 ones , if all ones cannot stand next to each other?
Let A = {2, 3, . . . , 50}, that is, A is the set of positive
integers greater than 1 and less than 51. Determine the smallest
number x such that every subset of A having x elements contains at
least two integers that have a common divisor greater than 1, and
justify your answer.
(5 marks) Let A {2,3, ,50}, that is, A is the set of positive integers greater than 1 and less than 51. Determine...
Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. (b) have distinct digits. (c) are not divisible by either 5 or 7.
How many whole numbers less than 10,000 contain the digit 5?
8. Define (n) to be the number of positive integers less than n and n. That is, (n) = {x e Z; 1 < x< n and gcd(x, n) = 1}|. Notice that U (n) |= ¢(n). For example U( 10) = {1, 3,7, 9} and therefore (10)= 4. It is well known that (n) is multiplicative. That is, if m, n are (mn) (m)¢(n). In general, (p") p" -p Also it's well known that there are relatively prime, then...
How many subsets are there of 5 letters? How many contain at least one letter, but not all of the letters {a, b, c, d, e}?
Write code that prints 500 random integers that are each less than 1000.