41 Answered Questions for the topic Combinatorics

Combinatorics Discrete Math Partitions


Prove that among all the 2^(n−1) compositions of n, the part k occurs a total of (n − k + 3)2^(n−k−2) times

Let 1 ≤ k < n. Prove that among all the 2n−1compositions of n, the part k occurs a total of (n − k + 3)2n−k−2 times. For instance, if n = 4 and k = 2, then the part 2 appears once in 2 + 1 + 1,... more
Combinatorics Discrete Math


A restaurant serves 10 different varieties of soup one of which is mushroom soup. In how many ways can we order six plates of soup if…

A restaurant serves 10 different varieties of soup one of which is mushroom soup. In how many ways can we order six plates of soup if (a) exactly four plates must be mushroom soup (b) at least four... more


finding an sum equation - Combinatorics

I need help finding an equation for the next formula and getting rid of the SUM sign
Combinatorics Probability Permutations


How many combinations of 16 characters can i have with 12 places? Repetition is allowed.

The game no man's sky has a coordinate system using "glyphs", unique characters, of which there are 16, but the actual coordinates only use 12 of these 16 glyphs.Repetition of glyphs are allowed.... more
Combinatorics Statistics Probability


Test preparation

A class is given 20 study problems from which 10 will be part of the exam. Student knows how to solve 15 of them. What are the chances that he will correctly answer:a) all 10b) exactly 8c) at least 9
Combinatorics Gre Permutations Gre Exam


GRE quant question (hard)?

"I got this question from the GRE book. Central state college has three sections of Math 102. If four students, Bill, Jill, Phill, and Will decide to transfer from Math 101 into Math 102, in how... more


Combinatorics Question

How many 6-character passwords can be created using the letters and numbers A, B, C, 1, 2, and 3 (each once) where the first character is a letter and the last character is a number?
Combinatorics Gre Probability Combinations


Combinations [fundemental counting principal]?

> How many 3-digit integers can be chosen such that none of the digits > appear more than twice and none of the digits equal zero? I have approached the following problem like this. 1. We... more

How are we able to calculate specific numbers in the Fibonacci Sequence?

I was reading up on the Fibonacci Sequence, $\ ext {{1,1,2,3,5,8,13,....}}$ when I've noticed some were able to calculate specific numbers. So far I've only figured out creating an array and... more
Combinatorics Gre Permutations Gre Exam


Combination GRE problem 25?

An appliance's model number consists of three alphanumeric characters. The first character must be one of 24 permissible letters of the alphabet. The next character is numeric, a digit from 1 to 9.... more


Intuition behind combination problem?

I came across this question on a GRE practice exam. I'm trying to build intuition behind how to correctly approach these types of problems: A reading list for a humanities course consists of 10... more
Combinatorics Gre Probability Gre Exam


combination gre problem # 24?

How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes? Can anyone explain me why this answer is wrong: 4*4*4 ?


Is the Maclaurin series expansion of $\\sin x$ related to the inclusion-exclusion principle?

When I see the alternating signs in the infinite series expansion of $\\sin x$, I'm reminded of the inclusion-exclusion principle. Could there be any way to visualize it in such a way? Also, is... more
Combinatorics Probability Counting


Probability and combinatorics questions

If there are 20 people with 17 men and 3 women and they seat themselves randomly at 4 Tables (A,B,C,D) with 5 people each. With all arrangements being equally likely, what is the probability that... more


11 different people and 11 rank places, how many distinct rank lists are possible with different rank places for every person?

11 different people and 11 rank places, how many distinct rank lists are possible with different rank places for every person?


You have 7 shirt and 4 ties. How many shirt-tie outfits can you make?

I need help answering this question .
Combinatorics Math Maths Math Help


Number arranging

The number of ways of arranging the 26 letters of the English alphabet = 26!. If a computer prints these arrangements at the rate of 1000 per second, how long will this take?


How many ways can I park 5 cars?

I have 5 cars (a BMW, a Chevy, a Fiat, a Honda, and a Kia) and 8 parking lots. How many ways can I distribute these over the available slots?   I thought the solution to the problem was simply... more
Combinatorics Math Probability Maths


Probability of winning raffle with multiple tickets (max one win each)

I have 90 tickets in a raffle.20,000 people have bought tickets.Each person has bought between between 60 and 100 tickets.The total number of tickets sold is 1,360,000 giving an average of 68... more


Determine the total number of ways...

Three students were selected from 23 senior students to be president, vice-president, and secretary of the student council. Three other students from 38 sophomore and junior students were also... more


Confusing combinatorics problem

A 4x5 grid has points A and C on opposite corners of the grid. Point B is 4 units east and 1 south from point A.   If the only allowed directions are south and east, what is the number of... more
Combinatorics Probability


Counting Two Pair 5-card Poker Hands

I'm trying to understand combinatorics and I'm having some trouble with the popular 'Two Pairs' problem. The question asks how many Two Pair hands can be made from a deck of 52.   I know the... more
Combinatorics Math Algebra 2 Probability


Probability of Getting a Test Question Correct Given Studying Some of the Possible Questions

A class is given a list of 20 study questions from which 12 will be part of their upcoming final. If a given student knows how to solve 15 of the problems, find the probability that the student... more

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