Permutations And Combinations - Class 11 Commerce Applied Mathematics - Extra Questions

In how many different ways can the letters of the word ' KURUKSHETRA' be arranged?



In how many different ways can the letters of the word `KURUKSHETRA' be arranged?



Prove that the number of ways in which $$8$$ different flowers can be strung to form a garland so that $$4$$ particular flowers are never separated is $$\dfrac{1}{2}4!4!$$



Determine the number of rectangles that can be formed on a chess-board.



There are p intermediate stations on a railway line from Delhi to Amritsar. In how many way can a super-fast train stop at three of these intermediate stations if no two of them are to be consecutive?



How many different words can be formed from the letters of the word GANESHPURI when:
The letter $$G$$ always occupies the first place.



How many different words can be formed from the letters of the word GANESHPURI when:
All the letters are taken.



How many $$2$$ digits numbers can be formed form the digits $$0,2,4,5,7$$ if the repetition o fthe digits (a)is not allowed (b)is allowed



In how many ways $$5$$ persons can sit at a round table, if two of the person do not sit together?



Find the number of $$5$$ lettered palindromes which can be formed using the letters from the English alphabets.



Find the number of different words formed with the letters of the word HARYANA.



Find the number of words each containing of $$3$$ consonants and $$3$$ vowels that can be formed from letters of the word Circumference. In how many of these all c's will be together.



Find the number of ways in which 410 different diamonds can be arranged to make a necklace.



No. of different 4 digit nos that can be formed with the digits 2,3,4,7 with repetition



Find the number of natural numbers which are less than $$2\times 10^{8}$$ and which can be written by means of the digit $$1$$ and $$2$$.



Show that a number of the form $$14^{n}$$, where $$n$$ is a natural number can never end with digit zero.



If $$\dfrac {^{ 56 }{ P }_{ r+6 }}{^{ 54 }{ P }_{ r+3 }}=30800:1$$, Find $$r$$.



If there are two jobs such that they can be performed independently in m and n ways respectively, then either of the two jobs can be performed in ....... ways.



The circular permutations of $$6$$ different things taken all at a time is .....



How many different words can be formed with the letters of the word HARYANA ?



Number of words formed, with or without meaning, using all the letters of the word EQUATION, using each letter exactly once is x!.Find the value of x.



In how many ways can the letter of the word $$PERMUTATIONS$$ can be arranged so that all the vowels come together



In how many ways can $$8$$ athletes finish a race for Gold Silver and Bronze medals?



How many 3 letter code can be formed by using the five vowels without repetitions? 



It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible? 



If the letters of the word $$MASTER$$ are permuted in all possible ways and the words thus formed are arranged in dictionary order, then find the rank of the word $$MASTER$$.



In how many ways $$4$$-digits numbers can be formed using the digits $$1,2,3,7,8,9$$ without repetition? How many of these are even numbers?



What is fundamental counting principle? What is the meaning of $$^{ n }{ P }_{ r }$$?



How many different ways can the letters of word CONSTITUTION be arranged? How many of these will have the letter $$N$$, both at the beginning and at the end?



Find the number of seven digited palindromes that can be formed using 0, 1, 2, 3, 4.



In how many ways can the letters of the word 'PERMUTATIONS' be arranged if the
(i) words start with $$P$$ and ends with $$S$$ and 
(ii) Vowels are all together.



There are 12 balls of which 4 are red, 3 black and 5 white: In how many ways can you arrange the balls so that no two white balls may occupy consecutive positions if balls of the same colour are identical?



How many different words can be formed from the letters of the word GANESHPURI when:
The letter $$P$$ and $$I$$ respectively occupy the first and last places.



A candidate is required to answer 6 out of 10 questions which are divided into two groups each containing 5 questions and he is not permitted to attempt more than 4 from each group. In how many ways can he make up his choice?



A businessman hosts a dinner to $$21$$ guests. He is having $$2$$ round tables which can accommodate $$15$$ and $$6$$ persons each. In how many ways can he arrange the guests?



Prove that at any time, the total number of persons on the earth who shake hands an odd number of times is even.



A person invites a party of $$10$$ friends at dinner and place them $$5$$ at one round table, $$5$$ at the other round table.$$4$$ at one round table and $$6$$ at other round table.The find the ratio, of number of circular permutations in case (i) to case (ii).~



How many four digit natural numbers not exceeding the number $$4321$$ can be formed using the digits $$1,\ 2,\ 3,\ 4,$$ if repetition is allowed?



Find the total number of permutation of $$k$$ different things in a row taken not more than $$r$$ at a time (each thing may be repeated any number of times ) 



In how many ways four men and three women may sit around a round table if all the women
i) always sit tohether
ii) never sit together



Find the distinct permutations of the letters of the word MISSISSIPPI?



In how many ways a child can select $$5$$ balls from $$4$$ black, $$3$$ white $$ ,2$$ green and $$1$$ yellow balls? (Assume balls of same color are identical)



The number of times the digit $$5$$ will be written while listing the integers from $$1$$ to $$1000$$ is $$xyz$$ then the value of $$(x + y + z)$$ is equal to 



Find the number of ways in which $$12$$ different flowers can be arranged in a garland so that.



How many six-digit odd numbers, greater than $$6,00,000$$, can be formed from the digits $$5, 6, 7, 8, 9$$ and $$0$$ if repetition of digits is allowed.



How many 4  letter words can be formed using the letters of the word PROPORTION.



In how many ways can $$8$$ persons be seated on two round tables of capacity $$5$$ & $$3$$.



How many numbers of five digits can be made with the digits $$1,2,3$$ each of which can be used at most thrice in a number?



Find the number of ways in which 5 men and 4 women can be seated on a round table, so that no two women are together.



How many three digits numbers can be formed from the digits $$0, 1, 3, 5, 6$$ if repetition of digits
i) are allowed ii) are not allowed?



In how many of the the distinct permutations of the letters in $$MISSISSIPPI$$ do the four $$I$$'s not come together?



In a group of students, $$100$$ students know Hindi, $$50$$ know English and $$25$$ know both. Each of students knows either Hindi or English. How many students are there in the group ?



How many natural numbers less than $$1000$$ can be formed from the digits $$0, 1, 2, 3, 4, 5$$ when a digit may be repeated any number of times?



How many $$4-digit$$ numbers are there, when a digit may be repeated any number of times?



What is the number of permutations of $$10$$ objects, taken $$4$$ at a time?



How many $$3-digit$$ numbers can be formed by using the digits $$0, 1, 3, 5, 7$$ while each digit may be repeated any number of times?



How many $$3-digit$$ numbers are there when a digit may be repeated any number of times?



How many $$3-digit$$ numbers above $$600$$ can be formed by using the digits $$2, 3, 4, 5, 6$$, if repetition of digits is allowed?



A child has plastic toys bearing the digits $$4, 4$$ and $$5$$. How many $$3-digit$$ numbers can he make using them?



How many $$4-digit$$ numbers can be formed with the digits $$0, 2, 3, 4, 5$$ when a digit may be repeated any number of times in any arrangement?



With $$17$$ consonants and $$5$$ vowels, how many words of four letters can be formed having $$2$$ different vowels in the middle and $$1$$ consonant (repeated or different) at each end?



Write all possible two-digit number using the digits $$4$$ and $$0.$$ repetition of digits is allowed.



Write all possible 2-digit numbers that can be formed by using the digit $$3, 7$$ and $$9.$$ Repetition of digits is allowed.



How many $$2$$-digit even numbers can be formed from the digits $$1 , 2 , 3 , 4 , 5 $$ if the digits , can be repeated ? 



How many $$3$$-digit numbers can be formed from the digits $$1 , 2 , 3 , 4 $$ and $$5$$ assuming that repetition of the digits is allowed ?



How many numbers can be formed using digits $$0, 1,2,....,9 $$ which is more than or equal to $$ 5000 $$ and less than $$ 6000 $$ and is divisible by $$ 5 $$ whereas any number can be repeated as many times?



How many numbers each lying between $$9$$ and $$1000$$ can be formed with the digits $$0, 1, 2, 3, 7, 8$$ if repetition of the digits in a number is allowed?



In how many different ways can $$4$$ married couples seat themselves around a circular table if (i) Spouses sit opposite each other? (ii) Men and women alternate?



Find the sum of all 4-digit numbers that can be formed using the digits 1, 2, 4, 6, 8. 



A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?



A team consist of $$6$$ boys and $$4$$ girls and other has $$5$$ boys and $$3$$ girls. How many single matches can be arranged between the two teams and a boys plays against a boys and girl plays against a girl?  



In how many ways can $$6$$ persons be arranged in a circle?



Class 11 Commerce Applied Mathematics Extra Questions