Permutation Combination

The number of distinct positive integers can be formed using $0,1,2,3$ where each integer used at most once is equal to

In an examination hall there are ' \(m n\) ' chairs in \(m\) rows and \(n\) columns. The number of ways in which \(m\) students can be seated such that no row is vacant is

Letters of the word 'GOVIND' are permuted and arranged as in a dictionary, then the number of words that appear after the word 'GOVIND' is ____

All the letters of the word ANIMAL are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word ANIMAL is \(x\), then the permutation with rank \(x\),…

The number of all four digit numbers which begin with 4 and end with either zero or five is

7 relatives of a man comprise 4 ladies and 3 gentlemen. His wife also has 7 relatives - 3 of them are ladies and 4 are gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen, so that…

$T_m$ denotes the number of triangles that can be formed with the vertices of a regular polygon of $m$ sides. If $T_{m+1}-T_m=15$, then $m$ is equal to

Six persons $A,B,C,D,E$ and $F$ are to be seated at a circular table facing towards the centre. Then the number of ways that can be done if $A$ must have either $E$ or $F$ on his immediate right and $E$ must have either…

The number of four-digit numbers formed by using the digits $0,2,4,5$ and which are not divisible by 5 , is

Among the 4 digit numbers formed using the digits $0,1,2,3,4$ when repetition of digits allowed, the number of numbers which are divisible by 4 is

The number of six digit natural numbers that can be formed with the digits $2,3,4,0,5,6,7,8$ is

The number of arrangements of the letters of the word ARRANGEMENT in which two Es' do not occur adjacently is