1.10 Counting principles and extended binomial theorem Quiz

1. In how many ways can a president, a secretary and a treasurer be chosen from 8 people?

• A. $56$
• B. $336$
• C. $512$
• D. $24$

2. In how many ways can a group of 3 be chosen from 8 people?

• A. $56$
• B. $336$
• C. $24$
• D. $6$

3. Find the coefficient of $x^2$ in the expansion of $(1+3x)^{-1}$.

• A. $-9$
• B. $3$
• C. $9$
• D. $-3$

4. For which values of $x$ is the expansion of $(2 - 5x)^{\frac12}$ valid?

• A. $|x| < \frac{5}{2}$
• B. $|x| < 1$
• C. $|x| < 2$
• D. $|x| < \frac{2}{5}$

5. Five different books are arranged on a shelf. In how many arrangements are two particular books next to each other?

• A. $24$
• B. $48$
• C. $120$
• D. $12$