X


Permutations and Combinations




Q. In how many ways can we select three students from a group of five students to stand in line for a picture? In how many ways can we arrange all five of these students in a line for a picture?



Permutation Formula :



Q. How many ways are there to select a first-prize winner, a second-prize winner, and a third-prize winner from 100 different people who have entered a contest?



Q. Suppose that there are eight runners in a race. The winner receives a gold medal, the second place finisher receives a silver medal, and the third-place finisher receives a bronze medal. How many different ways are there to award these medals, if all possible outcomes of the race can occur and there are no ties?



Q. Suppose that a saleswoman has to visit eight different cities. She must begin her trip in a specified city, but she can visit the other seven cities in any order she wishes. How many possible orders can the saleswoman use when visiting these cities?



Q. How many permutations of the letters ABCDEFGH contain the string ABC ?




Combinations




Q. How many poker hands of five cards can be dealt from a standard deck of 52 cards? Also, how many ways are there to select 47 cards from a standard deck of 52 cards?



Q. How many ways are there to select five players from a 10-member tennis team to make a trip to a match at another school?



Q. A group of 30 people have been trained as astronauts to go on the first mission to Mars. How many ways are there to select a crew of six people to go on this mission (assuming that all crew members have the same job)?



Q. How many bit strings of length n contain exactly "r" 1s?



Q. Suppose that there are 9 faculty members in the mathematics department and 11 in the computer science department. How many ways are there to select a committee to develop a discrete mathematics course at a school if the committee is to consist of three faculty members from the mathematics department and four from the computer science department?




The Binomial Theorem




Q. What is the expansion of (x + y)4?



Q. What is the coefficient of x12y13 in the expansion of (x + y)25 ?



Q. What is the coefficient of x12y13 in the expansion of (2x - 3y)25 ?



Q. How many strings of length "r" can be formed from the uppercase letters of the English alphabet?



Q. Suppose that a cookie shop has four different kinds of cookies. How many different ways can six cookies be chosen? Assume that only the type of cookie, and not the individual cookies or the order in which they are chosen, matters.




Combinations and Permutations With and Without Repetition: Formulae






Permutations with Indistinguishable Objects



Q. How many different strings can be made by reordering the letters of the word SUCCESS?



Distributing Objects into Boxes



Q. How many ways are there to distribute hands of 5 cards to each of four players from the standard deck of 52 cards?


Previous Next