Permutations

Which one of the following responses would be a meaningful order of the given words?

$1$. Imagination
$2$. Sculpture
$3$. Sculpt
$4$. Mud
$5$. Cast

A PSME unit has $10$ ME's, $8$ PME's and $6$ CPM's. If a committee of $3$ members, one from each group is to be formed, how many such committees can be formed?

There are four balls of four different colors. Two balls are taken at a time and arranged in a definite order. For example, if a white and red balls are taken, one definite arrangement is white first, red second, and another arrangement is red first, white second. How many such arrangements are possible?

How many $4$ digit numbers can be formed without repeating any digit from the following digits: $1,2,3,4 \& 6$ ?

In how many ways, six boys and six girls be seated in a row alternatively ?

Which one of the following words will come Second from right if they are arranged according to the dictionary ?

In how many ways can $6$ distinct books be arranged in a bookshelf?

In how many ways, six boys and three girls be seated in a row so that the three girls do not sit together?

If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be

How many permutations are there if the letters PNRCSE are taken six at a time?

Which of the following numbers will completely divide$(3^{19} + 3^{20} + 3^{21} + 3^{22}) ?$

What is the number of permutations of the letters in the word BANANA?

Let $X$  be a set with exactly $5$ elements and $Y$ be a set with exactly $7$ elements. If $\alpha$ is the number of one-one functions from $X$ to$Y$ and $\beta$ is the number of onto functions from $Y$ to  $X$ , then the value of $\frac{1}{5!}\left(\beta -\alpha \right)$ is

A flight of stairs has 10 steps. A person can go up the steps one at a time, two at a time, or any combination of 1's and 2's. Find the total number of ways is in which the person can go up the stairs.

The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently, is

Eighteen guests have to be seated half on each side of a long table. Four particular guests desire to sit on one particular side and three other on the other side. Determine the number of ways in which the sitting arrangements can be made.

Consider all the permutation of the word JANLOKPAL number of words which O never lies between J and N.

There are four hotels in a town. If $3$ men check into the hotels in a day, then what is the probability that each checks into a different hotel$?$

Let the digits $a, b, c$ be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?