The number of different ways in which five "alike dashes" and "eight alike" dots can be arranged using only seven of these "dashes" and "dots" is

The number of ways in which n things of which r are alike,can be arranged in a circular order, is

The number of different messages produced by using five signals with three dots and two dashes is

Number of ways in which n things of which r alike delta the rest different can be arranged in a circle distinguishing between clockwise and anticlockwise arrangement,is

Which of the following number of dots cannot be arranged as a triangle?

Find the number of ways in which the letters of word KUTKUT Can be arranged So that no two alike letters are together.

Consider the word W = COMMISSIONER Find (i) Number of 5 letters word containing two vowels and three consonants. Number of ways in which all the letters of the word W can be arranged if alike letters are together but seperated from the other alike letters (iii) Number of ways in which letters of the word W can be arranged without changing order of alike letters.

Which of the following number of dots cannot be arranged as a rectangle?

Let m denote the number of ways in which 4 different books are distributed among 10 persons,each receiving none or one only and let n denote the number of ways of distribution if the books are all alike.Then

There are five different boxes and seven different balls.All the seven balls are to be distributed in these boxes.The number of ways can they be distributed so that no box remains empty are