Permutations and Combinations
Given 5 flags of different colours, how many different signals can be generated if each signal require use of 2 flags one below the other?
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A five-digit number divisible by 3 is to be formed using the digits 0,1,2,3,4,and5, without repetition. The total number of ways this can done is (a) 216 (b) 240 (c) 600 (d) 3125
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
The streets of a city are arranged like the like the lines of a chess board. There are m
streets running from north to south and n
streets from east to west. Find the number of ways in which a man can travel from north-west to south-east corner, covering shortest possible distance.
If N denotes the number of ways of selecting r objects of out of n distinct objects (r≥n) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .r−1Cr−n
b. .r−1Cn c. .r−1Cn−1
d. none of these
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
10 different letters of an alphabet are given. Words with 5 letters are formed from these given letters then the numbers of words which have atleast one letter represent is: