Trial

//

01_COMBINATORICS_ALL_MIXED

Name

Email

Untitled section

Ten points are marked on a circle. How many distinct convex polygons of three or more sides can be drawn using some (or all) of the ten points as vertices?

A subset B of a set of first 100 positive integers has the property that no two elements of B sum 125. What is the maximum possible value of B?

How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold?- the vowels occur in the same order (EUAIO)- the consonants are next to ea ch other (DCTN)- no two consonants are next to each other.

Words of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let x be the number of such words where no letter is repeated and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, y/9x is equal to

A closet has 5 pairs of shoes find the number of ways in which 4 shoes can be drawn from it such that there will be no complete pair.

The sides AB, BC, CA of a triangle ABC have 3,4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices.

Father has left to his children several identical gold coins. According to his will, the oldest child receives one coin and one-seventh of the remaining coins, the next child receives two coins and one-seventh of remaining coins, the third child receives three coins and one-seventh of the remaining coins, and so on through the youngest child. If every child inherits an integer number of coins then find the sum of number of children and coins.

This is a difficult problem with concept of recurrence series, don't be upset if you are not able to solve it.