State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. Hugo displays his 8 model planes in a single row.

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. A student chooses at random 4 books from a reading list of 11 books.

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. At the end of a season, 10 soccer teams are ranked by the state.

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. At the end of a season, 10 soccer teams are ranked by the state.

Find the number of combinations. In how many ways can 11 contestants for an award be narrowed down to 3 finalists?

Calculate

$$\iint _ { \mathcal { S } } f ( x , y , z ) d S$$

for the given surface and function.

$$G ( u , v ) = \left( u , v ^ { 3 } , u + v \right), \quad 0 \leq u \leq 1,0 \leq v \leq 1;$$

f(x, y, z) = y

Decide whether the statement is true or false. Give an explanation for your answer. To calculate $\int \frac { 1 } { x ^ { 3 } + x ^ { 2 } } d x,$ we can split the integrand into $\int \left( \frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x + 1 } \right) d x.$

Solve the problem by writing and solving an equation. Three friends share the cost of renting a game system. Each person also rents one game for $8.50. If each person pays$13.25, what is the cost of renting the system?

Students will be chosen at random for school spirit awards. There are 6 athletes and 8 non-athletes who are eligible for 2 possible prizes. What is each probability? P(no prize is awarded to a non-athlete)

Permutation or combination? A student chooses at random 4 books from a reading list of 11 books. Show and solve the equation.

Dwayne bought a new bike lock, and the lock came with instructions to choose 3 out of 30 numbers on a circular dial to keep his bike secure. The numbers cannot be repeated. How many possible arrangements can Dwayne choose for his lock? Do the arrangements represent permutations or combinations? Explain.

Students will be chosen at random for school spirit awards. There are 6 athletes and 8 non-athletes who are eligible for 2 possible prizes. What is each probability? P(no prize is awarded to an athlete)

Students will be chosen at random for school spirit awards. There are 6 athletes and 8 non-athletes who are eligible for 2 possible prizes. What is each probability? P(both prizes are awarded to non-athletes)

Students will be chosen at random for school spirit awards. There are 6 athletes and 8 non-athletes who are eligible for 2 possible prizes. What is each probability? P(both prizes are awarded to athletes)