Binomial Series - Ambitious

Question 1: Find the value of

\frac{16!}{13!}

A

\frac{16}{13}

B

240

C

3360

D

0

Question 2: Find the value of

\frac{4!}{0!}

A

0

B

Does not exist

C

24

D

1

Question 3: Knowing that combinational coefficient

C_{r}^{n} = \frac{n!}{(n - r)! r!}

, find

C_{1}^{5}

A

5

B

1

C

25

D

0

Question 4: Simplify:

\frac{(3 n)!}{(3 n + 2)!}

A

\frac{1}{(3 n + 3) (3 n + 2)}

B

\frac{1}{{(3 n + 3)}^{2}}

C

\frac{1}{(3 n + 2) (3 n + 1)}

D

\frac{3 n}{3 n + 2}

Question 5: Find the coefficient of

x^{4}

in the binomial expansion of

{(2 - \frac{3}{x})}^{9}

A

\frac{1}{x^{4}}

B

\frac{353682}{x^{4}}

C

\frac{326592}{x^{4}}

D

\frac{647378}{x^{4}}

Test: Binomial Series - Ambitious