\begin{tabular}{l} Pre-Cal 12 - Chapter 11 Assignment \ \hline Name: \ $$ \begin{array}{ll} ext { 1. The number of different ways that } 9 ext { bikes can be locked in a bike rack is } \ ext { B. } 2628800 & ext { C. } 40320 \ ext { B. } 20160 & ext { D. } 362880\end{array} $$ \ $$ \begin{array}{ll} ext { 3. After the tryouts for the volleyball team, the coach selects } 14 ext { people to join the team. Due to a problem with } \ ext { transportation, only } 9 ext { people can travel. In how many ways can the coach pick the people to go? } \ ext { A. } 726485760 & ext { C. } 630 \ ext { B. } 2002 & ext { D. } 126\end{array} $$\end{tabular}

Question

\begin{tabular}{l} Pre-Cal 12 - Chapter 11 Assignment \ \hline Name: \ $$ \begin{array}{ll}	ext { 1. The number of different ways that } 9 	ext { bikes can be locked in a bike rack is } \ 	ext { B. } 2628800 & 	ext { C. } 40320 \ 	ext { B. } 20160 & 	ext { D. } 362880\end{array} $$ \ $$ \begin{array}{ll}	ext { 3. After the tryouts for the volleyball team, the coach selects } 14 	ext { people to join the team. Due to a problem with } \ 	ext { transportation, only } 9 	ext { people can travel. In how many ways can the coach pick the people to go? } \ 	ext { A. } 726485760 & 	ext { C. } 630 \ 	ext { B. } 2002 & 	ext { D. } 126\end{array} $$\end{tabular}

UpStudy AI · Accepted Answer

To solve the given problems, we will use the concept of permutations and combinations.

1. The number of different ways that 9 bikes can be locked in a bike rack:
   - This is a permutation problem since the order of the bikes matters.
   - The number of permutations of n objects taken r at a time is given by $$ P(n, r) = \frac{n!}{(n-r)!} $$.
   - In this case, n = 9 (number of bikes) and r = 9 (number of bikes to be locked).
   - Therefore, the number of different ways that 9 bikes can be locked in a bike rack is $$ P(9, 9) = \frac{9!}{(9-9)!} = 9! = 362880 $$.

2. The coach selects 14 people to join the team, but only 9 people can travel:
   - This is a combination problem since the order of the people does not matter.
   - The number of combinations of n objects taken r at a time is given by $$ C(n, r) = \frac{n!}{r!(n-r)!} $$.
   - In this case, n = 14 (number of people selected) and r = 9 (number of people who can travel).
   - Therefore, the number of ways the coach can pick the people to go is $$ C(14, 9) = \frac{14!}{9!(14-9)!} = \frac{14!}{9!5!} = 126 $$.

So, the answers are:
1. The number of different ways that 9 bikes can be locked in a bike rack is 362880.
2. The number of ways the coach can pick the people to go is 126.
1. There are 362880 different ways to lock 9 bikes in a bike rack. 2. The coach can pick the people to go in 126 ways.

Pre-Cal 12 - Chapter 11 Assignment

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