Permutation

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?

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.

Show that $\frac{12!}{5!7!}+\frac{12!}{6!6!}=\frac{13!}{6!7!}$

Among the inequalities below, which ones are true for all natural numbers $n$ greater than $1000$ ?
I. $n!\le n^n$
II. ${\left(n!\right)}^2\le n^n$
III. ${10}^n\le n!$
IV. $n^n\le \left(2n\right)!$

The largest power of $2$ that divides $\frac{200!}{100!}$ is

The number of ways in which $x$ Boys and $y$Girls can be seated in a row such that $2$ Girls always sit together is _____.

If $x+y=12$ and both $x$ and $y$ are prime numbers______.

There is a word $\mathrm{CARIHT}$ in the comedy book and if the letters of the word $\mathrm{CARIHT}$ are arranged in all possible ways as listed in dictionary. Then what is the rank of the word $\mathrm{CARIHT}$?

How many One time passwords can be made if each One time password contains two different letters followed by three different digits?