6. How many positive integer's 5 301 that are multiple of at least of one of...
how many positive integers less than 1000 are there which contain one 4 or at least one 9 (or both)
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}?
5. How many even positive integers are there that are divisors of 30030? 6. Suppose 6 identical dice each with faces numbered 1 through 6 are tossed at the same time. What is the probability of the event "the result of the outcome is such that three different numbers each appear twice?" At
8. (i) How many positive integers not exceeding 200 that are divisible by 3 or 5 are there? (ii) What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?
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...
Problem 2 a) In how many ways can 6 women and 5 men line up so that no two men are next to one another? b) In how many ways can 7 different pairs of twins line up so that twins must be next to one another? c) In how many ways can 7 women and 10 men sit at a circular table so that no two women are sitting side by side? d) How many strings of length 5...
Exercise 6: How many positive integers between 1 and 10", with n 1 a positive integer, does not have 7 as a digit in their base 10 representation?
In how many ways can one obtain at least three jacks in a six card hand? Example: A card is drawn from an ordinary deck. [#5-8]
Show your work, please
5. Binomial Coefficients (a). How many subsets with at least 5 elements does a set with 8 elements have? (b). Find the coefficient of 2" in (3 - 2.c)"+3 (c). How many ways are there to walk down from the top of Pascal's Triangle and end somewhere on the number 20?
How many different kinds of protons are present in the following molecule? Multiple Choice 2 5 X 4 3