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Evaluate the following:

${}^{10}{P_4}$

${}^{10}{P_4}$

Find the value of \[{^8}{P}{{_8}}\]

If we have an expression \[^{n}{{C}_{12}}{{=}^{n}}{{C}_{6}}\], then \[^{n}{{C}_{2}}\]?

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

$

A.\;5!\; \times \;5! \\

B.\;4!\; \times \;5! \\

C.\;\dfrac{{5!\; \times \;5!}}{2} \\

$

$D.$ None of these

$

A.\;5!\; \times \;5! \\

B.\;4!\; \times \;5! \\

C.\;\dfrac{{5!\; \times \;5!}}{2} \\

$

$D.$ None of these

How many words, with or without meaning can be formed using all the letters of the word EQUATION, using each letter exactly once?

How do you evaluate ${}_{7}{{P}_{7}}$?

If we are given the ratio of permutation as ${}^{n}{{P}_{4}}:{}^{n}{{P}_{5}}=1:2$, then $n$ is:

1. 4

2. 5

3. 6

4. 7

1. 4

2. 5

3. 6

4. 7

If $P_m$ stands for $mP_m$, then $1+1p_1+2P_2+3P_3+…+n.P_n$ is equal to:

A man has 5 friends. In how many ways can he invite one or more of them to a tea party?

$

(a){\text{ 30}} \\

(b){\text{ 31}} \\

(c){\text{ 32}} \\

(d){\text{ 25}} \\

$

$

(a){\text{ 30}} \\

(b){\text{ 31}} \\

(c){\text{ 32}} \\

(d){\text{ 25}} \\

$

The letters of the word RANDOM are written in all possible orders and these words are written out as in a dictionary then the rank of the word RANDOM is.

A.$614$

B.$615$

C.$612$

D.$616$

A.$614$

B.$615$

C.$612$

D.$616$

How many different arrangements can be made using all of the letters in the word REARRANGE?

How many permutations of the letters “a b c d e f g h” contain?

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