Pre-Cal 12 - Chapter 11 Assignment
Name:

The number of different ways that 9 bikes can be locked in a bike rack is
A. 3628800
C. 40320
B. 20160
D. 362880

After the tryouts for the volleyball team, the coach selects 14 people to join the team. Due to a problem with transportation, only 9 people can travel. In how many ways can the coach pick the people to go?
A. 726485760
C. 630
B. 2002
D. 126
_ 5. For a mock United Nations, 6 boys and 7 girls are to be chosen. If there are 12 boys and 9 girls to choose from, how many groups are possible?
A. 846720
C. 960
B. 33264
D. 120708403200

Determine the coefficient of the term containing in the binomial expansion of .
A. 35
C. 792
B. 60
D. 3991680

Determine the 5 th term in the expansion of .
A.
C.
B.
D.

How many terms are there in the expansion of ?
A. 6
C. 12
B. 13
D. 11

The leadership committee at a high school has 4 grade 10 students, 2 grade 11 students, and 6 grade 12 students. This year, 12 grade 10,8 grade 11 , and 10 grade 12 students applied for the committee. How many ways are there to select the committee?
A. 2910600
C. 733
B. 100590336000
D. 163136

While at the dollar store, Peter finds 19 items at each that he wants, but he only has . The number of ways he could select which items to buy is
A.
C.
B.
D.

Solve for the variable. Algebraic work must be shown.

Ask by Martin Craig. in the United Arab Emirates

Jan 13,2025

Question

Pre-Cal 12 - Chapter 11 Assignment
Name:

The number of different ways that 9 bikes can be locked in a bike rack is
A. 3628800
C. 40320
B. 20160
D. 362880

After the tryouts for the volleyball team, the coach selects 14 people to join the team. Due to a problem with transportation, only 9 people can travel. In how many ways can the coach pick the people to go?
A. 726485760
C. 630
B. 2002
D. 126
_ 5. For a mock United Nations, 6 boys and 7 girls are to be chosen. If there are 12 boys and 9 girls to choose from, how many groups are possible?
A. 846720
C. 960
B. 33264
D. 120708403200

Determine the coefficient of the term containing in the binomial expansion of .
A. 35
C. 792
B. 60
D. 3991680

Determine the 5 th term in the expansion of .
A.
C.
B.
D.

How many terms are there in the expansion of ?
A. 6
C. 12
B. 13
D. 11

The leadership committee at a high school has 4 grade 10 students, 2 grade 11 students, and 6 grade 12 students. This year, 12 grade 10,8 grade 11 , and 10 grade 12 students applied for the committee. How many ways are there to select the committee?
A. 2910600
C. 733
B. 100590336000
D. 163136

While at the dollar store, Peter finds 19 items at each that he wants, but he only has . The number of ways he could select which items to buy is
A.
C.
B.
D.

Solve for the variable. Algebraic work must be shown.

Ask by Martin Craig. in the United Arab Emirates

Jan 13,2025

UpStudy AI · Accepted Answer

To solve for $$ r $$ in the permutation equation:

$$
{}_{5}P_{r} = 20
$$

we'll use the permutation formula:

$$
{}_{n}P_{r} = \frac{n!}{(n - r)!}
$$

**Step 1: Plug in the known values**

Given $$ n = 5 $$ and $$ {}_{5}P_{r} = 20 $$, the equation becomes:

$$
\frac{5!}{(5 - r)!} = 20
$$

**Step 2: Calculate $$ 5! $$**

$$
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
$$

So the equation is:

$$
\frac{120}{(5 - r)!} = 20
$$

**Step 3: Solve for $$ (5 - r)! $$**

$$
\frac{120}{(5 - r)!} = 20 \quad \Rightarrow \quad (5 - r)! = \frac{120}{20} = 6
$$

**Step 4: Determine the value of $$ (5 - r) $$ that satisfies the factorial**

We know that:

$$
3! = 6 \quad \text{and} \quad 2! = 2
$$

So,

$$
5 - r = 3 \quad \Rightarrow \quad r = 5 - 3 = 2
$$

**Conclusion**

$$
r = 2
$$
$$ r = 2 $$