Combinatorics | Number Theory Answers

100 to the power of 3

How many 3 digit positive even integers are there, such that all the digits are distinct from each other?
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6 friends (Andy, Bandy, Candy, Dandy, Endy and Fandy) are out to dinner. They will be seated in a circular table (with 6 seats). Andy and Bandy want to sit next to each other to talk about the Addition Principle, Bandy and Candy want to sit next to each other to talk about the Principle of Inclusion and Exclusion. How many ways are there to seat them?
Clarification: Rotations are counted as the same seating arrangements, reflections are counted as different seating arrangements.

Muffins are in packages of 1, 2, 3, 4 and 6. How many combinations to equal 10?

problem: During a treasure hunt organized by the school's afterschool program, 124 children form groups of four. How many groups are there in total?

Question: Is this partitive (also known as sharing) or measurement (also known as quotative) ? explain your answer

how many zero"s are there in tha result of 1!*2!*3!.......99!

give m a shortcut(or formula)to solve suvh kind of problem

If only four numbers were used in a license and a digit 0-9 could only be used once per plate, how many different plates can be produced?

Suppose You have eight televisions. Three are defective. If teo are randomly selected, compute the probability that both televisions work. What is the probability that at least one of the two does not work?

Peter picked 4 positive integers a,b,c and d. He wanted to determine the polynomial f(x)= (1−x)^(a+b+c+d)(1+x)^(a+b+c)(1−x+x2)^(a+b)(1+x+x2)^a. He felt lazy and ignored any term that involved x taken to a power larger than 4. He was surprised to see that the result was the term . What is the value of ?

There are 20 people on the board of directors of a publicly listed company. Each pair of people are either friends or enemies with each other. Every person has exactly 6 enemies on the board. If every group of 3 directors form a committee, what is the total number of committees that are formed by all friends or all enemies?