Permutation Combination

A number is called a palindrome if it reads the same backward as well as forward. For example $285582$ is a six digit palindrome. The number of six digit palindromes, which are divisible by $55,$ is ________?

Consider a rectangle $ABCD$having $5,6,7,9$ points in the interior of the line segments $AB,BC,CD,DA$ respectively. Let $\alpha\,$ be the number of triangles having these points from different sides as vertices and…

The number of ways,$16$ identical cubes, of which$11$ are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least$2$ blue cubes, is ______?

If the digits are not allowed to repeat in any number formed by using the digits $0,2,4,6,8,$ then the number of all numbers greater than $10,000$is equal to __________.

The number of natural numbers lying between$1012$ and $23421$ that can be formed using the digits $2,3,4,5,6$ (repetition of digits is not allowed) and divisible by $55$is _____?

The total number of numbers, lying between $100$ and $1000$ that can be formed with the digits $1,2,3,4,5,$ if the repetition of digits is not allowed and numbers are divisible by either $3$ or $5,$ is

The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , is

Three persons enter in a lift at the ground floor. The lift will go upto $10^{\text {th }}$ floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at…

Let ABC be a triangle. Consider four points $\mathrm{p}_{1}, \mathrm{p}_{2}, \mathrm{p}_{3}, \mathrm{p}_{4}$ on the side AB, five points $p_{5}, p_{6}, p_{7}, p_{8}, p_{9}$ on the side $B C$, and four points $p_{10},…

All words, with or without meaning, are made using all the letters of the word $MONDAY$. These words are written as in a dictionary with serial numbers. The serial number of the word $MONDAY$ is

The total number of words (with or without meaning) that can be formed out of the letters of the word "DISTRIBUTION"taken four at a time, is equal to ______?

The number of permutations, of the digits $1,2,3,\ldots\,,7$ without repetition, which neither contain the string $153$ nor the string $2467$, is _______ ?