Permutation & combination Definition and 12 Threads

The rightmost position has 3 possibilities: ##x,y,z## The remaining two letters are to be arranged in 6 spaces: ##\frac{6!}{4!}## Now the 3 can be placed in ##\frac{4!}{3!}## Total no of ways =$$3×\frac{6!}{3!}=12×30$$ $$OR$$ Since ##x,y,z## are three different boxes/variables, we can use the...

Hello! I am looking for textbooks to relearn Combinatorics, Permutations Combinations and Probability and also Matrix algebra( decomposition, etc). I had done these many years ago and the course/books provided to me at that time weren't that great. So I want to relearn this with a more...

I have a question and searched about at google and found an answer which I don't make sure. If there is 26 letters and 10 digits; my answer is: first letter: 1 way(which is A) second letter: 26 way third letter: 26 way first digit: 1 way(which is 1) second digit 1 way(which is 2) third digit: 10...

Hi folks - I need some help with a tricky probability. Here's the situation: Let's say there are 4M internet users in Age Group A. (The total set) Of those 4M, there are 1,000 users who play a specific sport. Those 1,000 are spread evenly over 125 teams, so 8 players each. 1. What's the...

I know how to find integral solutions of linear equations like x+y=C or x+y+z=C where C is a constant. But I don't have any idea how to solve these type of questions.I am only able to predict that both x and y will be greater than 243554.Please help.

Homework Statement The back row of a cinema has 12 seats, all of which are empty. A group of 8 people including Mary and Francis, sit in this row. Find the number of ways they can sit in these 12 seats if a) There are no restrictions b) Mary and France's do not sit in seats which are next to...

Homework Statement There is a book with 2 volumes. Each volume exists in 3 different languages. Each language has 2 identical copies(total of 12 books). In how many ways we can arrange them on a shelf, with no restrictions and order of the volumes is irrelevant? Homework EquationsThe Attempt...

.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is (1) 901 (2) 861 (3) 820 (4) 780 my attempt: for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.

If there was a 1 billion x 1 billion x 1 billion cube made of 3D pixel cubes, and half of them are black and half of them are clear/colorless, then how many combinations of unique pixel arrangements are there? Would the amount of shapes/objects in this cube be infinite? (Assuming the black...

Homework Statement There are 30 students in a class. In how many ways can we arrange them if : a)we must have three group, group one must have 5 students , group two 10 students and group three 15 students. answer=\frac{30!}{5!*10!*15!} b)we must have three group and all must have 10 students...

Homework Statement From the numbers 4,5,6,8,9 we make 5 digits numbers (each number can be used only once). h)How many of these numbers are divisible by 8? The correct answer is 20 Homework Equations a number is divisible by 8 if the last 3 digits are divisible by 8 If the hundreds digit is...

Let me phrase the problem in a general way. Given n objects in a set. All the objects can be categorized into k groups such that no two objects from different groups are identical. Objects in the same group are indistinguishable from each other within the group. Number of objects in each...