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

In how many ways can $5$ people line up to pay their electric bills?

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?

Eight Friends A, B, C, D, E, F, G and H are sitting around a circular table facing the centre not necessarily in the same order. B is second to the right of A. B is to the immediate left of H. D is second to right of B. C is fourth to left of H. F is an immediate neighbour of D. E is not an immediate neighbour of A.

Who is sitting exactly between E and A ?

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?

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.

How many words comprising of any three letters of the word UNIVERSAL can be formed?

If ${}^{n}p_6=20{}^{n}p_4$ then the value of $n$ is given by

If ${}^{n}P_4={20}^n{P}_2$ where $P$ denotes the number of permutations, then $n=$ ________