Permutation and combination practice · Mixed difficulty

The number of ways in which a couple can sit around a table with 6 guests, if the couple take consecutive seats, is

The value of $\left({ }^7 C_0+{ }^7 C_1\right)+\left({ }^7 C_1+{ }^7 C_2\right)+\ldots+\left({ }^7 C_6+{ }^7 C_7\right)$ is

There are three copies each of 4 different books. The number of ways in which they be arranged on a shelf is

Ten persons are arranged in a row. The number of ways of selecting four persons so that no two persons sitting next to each other are selected is

How many words can be formed from the letters of the word ARTICLE, if vowels always comes at the odd places?

The total number of 4-digit numbers that are greater than 3000, that can be formed using the digits $1, 2, 3, 4, 5, 6$ (no digit is being repeated in any number) is equal to

The number of ways can 14 identical toys be distributed among three boys, so that each one gets atleast one toy and no two boys get equal number of toys, is

If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fifteen word is

Number of number greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1, 2, 3, 4, are

Find $n$ if ${ }^{n-1} P_3:{ }^n P_4=1: 9$

The 3 digit numbers which are divisible either 3 or
4 but not divisible by 48

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is

The number of ways in which the letters of 'ARRANGE' be arranged so that "Two R's come together and Two A's come together is

The number of times of the digits 3 will be written when list- ing the integers from 1 to 1000 is

The total number of permutations of $n( > 1)$ different things taken not more than r at a time, when each thing may be repeated any number of times is

The number of ways in which the letters of word FRACTION be arranged so that no two vowels are together, is

The number of numbers of 9 distinct digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is

The total number of functions, $f:\{1,2,3,4\} \rightarrow\{1,2,3,4,5,6\}$ such that $f(1)+f(2)=f(3)$, is equal to

Number greater than 1000 but less than 4000 is formed using the digits $0,1,2,3,4$ (repetition allowed). Their number is

The number of ways in which 30 marks can be alloted to 8 questions if each question carries at least 2 marks, is

For the post of 5 teachers there are 23 applicants, 2 posts are reserved for S. C. candidates and there are 7 S.C. candidates among the applicants. The number of ways in which the selection can be made is

The number of ways in which a mixed doubles game in tennis can be arranged from 5 married couples, if no husband and wife play in the same game, is

The number of ways in which a committee of 5 can be chosen from 10 candidates so as to exclude the youngest, if it includes the oldest, is

On a New Year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class is

The number of ways in which 6 rings can be worn on four fingers of one hand, is

The value of $1.1! + 2.2! + 3.3! + ... + n.n!$ is

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

The number of ways of arranging 20 boys so that 3 particular boys are separated is

The number of 4 letter words that can be formed from letters of the word 'PART', when:

Statement I: Repetition is not allowed is 24.

Statement II: Repetition is allowed is 256.

Which of the above statement(s) is/are true?

The number of ways we can put 5 different balls in 5 different boxes such that at most three boxes is empty, is equal to