Permutation and combination practice · Easy

20 persons are invited for a party. In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

Let $m$ and $n$ be two digit natural numbers. The number of pairs $(m, n)$ such that $n$ can be subtracted from $m$ without borrowing is:

If ${\;^{56}}{P_{r + 6}}\;:{\;^{54}}{P_{r + 3}} = 30800:1$, then the value of $r$ is

If $m = {\;^n}{C_2}$, then ${\;^m}{C_2}$ is equal to

Find the number of 5 digited numbers that can be formed using 2, 2, 3, 3, 4

The least positive integral value of $x$ which satisfies the inequality ${ }^{10} {C}_{x-1}>2 .{ }^{10} {C}_x$ is

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

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

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 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 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 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 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

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 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

The number of maps (functions) from the set $A=\{1,2,3\}$ into the set $B=\{1,2,3,4,5,6,7\}$ such that $f(i) \leq f(j)$ whenever $i < j$, is

How many even numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition of digits is not allowed)?

How many arrangements can be made out of the letters of the word &quot; MOTHER&quot; taken four at a time so that each arrangement contains the letter &#39; $\mathrm{M}^{\text {'? }}$

The value of $\sum\limits_{{r=1}}^n \frac{{ }^n P_r}{r !}$ is

There are 3 candidates for a post and one is to be selected by the votes of 7 men. The number of ways in which votes can be given, is

The number of other ways in which the letters of the work SIMPLETON can be rearranged is