Help me with 1 through 7 please and thank you

An elevator containing five people can stop at any of seven floors. What is the probability that no two people exit at the same

elena-s [515]

Answer:

Approximately $0.15$ ( $360 / 2401$ .) (Assume that the choices of the $5$ passengers are independent. Also assume that the probability that a passenger chooses a particular floor is the same for all $7$ floors.)

Step-by-step explanation:

If there is no requirement that no two passengers exit at the same floor, each of these $5$ passenger could choose from any one of the $7$ floors. There would be a total of $7 \times 7 \times 7 \times 7 \times 7 = 7^{5}$ unique ways for these $5\!$ passengers to exit the elevator.

Assume that no two passengers are allowed to exit at the same floor.

The first passenger could choose from any of the $7$ floors.

However, the second passenger would not be able to choose the same floor as the first passenger. Thus, the second passenger would have to choose from only $(7 - 1) = 6$ floors.

Likewise, the third passenger would have to choose from only $(7 - 2) = 5$ floors.

Thus, under the requirement that no two passenger could exit at the same floor, there would be only $(7 \times 6 \times 5 \times 4 \times 3)$ unique ways for these two passengers to exit the elevator.

By the assumption that the choices of the passengers are independent and uniform across the $7$ floors. Each of these $7^{5}$ combinations would be equally likely.

Thus, the probability that the chosen combination satisfies the requirements (no two passengers exit at the same floor) would be:

$\begin{aligned}\frac{(7 \times 6 \times 5 \times 4 \times 3)}{7^{5}} \approx 0.15\end{aligned}$ .

5 0

2 years ago

What are the expressions to fin the radius of an object having a circumference of 46 feet

dolphi86 [110]

Since the equation for solving circumference is 2 $\pi$ r, you can see that 2 $\pi$ r = 46. Dividing 2 $\pi$ on both sides will give you r, or the radius.
Hope this helped! :)

3 0

3 years ago

At 10 A.M the outside temperature was -5 F. By noon, the temperature was -17 F. Ricardo said that it was getting warmer outside.

Natasha_Volkova [10]

Ricardo is not correct because the temperature is actually getting colder (idk if I need to explain it more). The difference is -12 F

8 0

3 years ago

Read 2 more answers

A library charges a late return fee of 3.50 plus $0.15 per day that a book is returned late write a equation to find the total l

joja [24]

The equation would be:

3.50 + 0.15x

x represents each 'late day'

7 0