##### Question

In: Statistics and Probability

# statistics question

In the Olympics, there are 8 swimmers in the final race. How many ways can the gold, silver, and bronze medals be distributed among the 8 contestants?

## Solutions

##### Expert Solution

Step 1

Counting rule: when we selecting elements of a set, then the number of possible outcomes depends on the conditions under which the selection has taken place. there are four types of rules to count the number of possible outcomes:

1) Multiplicative rule

2) Permutation rule

3) Partitions rule

4) Combination rule

Step 2

There are 8 swimmers in the final race. here we want to know that, how many ways can gold, silver, and bronze medals be distributed among 8 contestants.

Therefore, by using the counting rule, there are 8 choices for the gold medal winner, 7 remaining choices for silver, and 6 for the bronze, so there are 8××7××6 = 336 ways the three medals can be awarded to the 8 winners.

Therefore, by using the counting rule, there are 8 choices for the gold medal winner, 7 remaining choices for silver, and 6 for the bronze, so there are 8××7××6 = 336 ways the three medals can be awarded to the 8 winners.

## Related Solutions

##### physics question
A toy car with a mass of 1 kg starts from rest at the top of a ramp at point A. The toy car is released from rest, rolls 2.0 meters down the ramp, then another 3.0 meters across the floor to point B where its speed is measured to be 4.24 m/s. The air exerts a resistance force of 2.0 N on the car as it moves from A to B. Find the initial height of the car at...
##### Logical Question
Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 650 victims consists of evil sorcerers, trolls, and orcs. These he has slain with a total of 700 mighty thrusts of his sword; evil sorcerers and trolls each requiring two thrusts (to the chest) and orcs each requiring one thrust (to the neck). When asked about the number of trolls he has slain, he replies, "I,...
##### Question on work energy and power.
A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with the coefficient of kinetic friction = 0.1. Compute the following (a) work done by the applied force in 10 s, (b) work done by friction in 10 s, (c) work done by the net force on the body in 10 s, (d) change in kinetic energy of the body in 10 s,
##### Physical Chemistry chemical equilibrium question
Dissociation of phosphorus pentachloride $$\left(P C I_{5}\right)$$ is favored by- (i)High T, High P (ii) High T, low P (iii) Low T, Low P (iv) Low $$T$$, High P
##### Multiple Choice question on Auditor's Report
The section of the annual report that is the report of the independent registered public accounting firm is often referred to as the  A. Auditor's Report B. Management's discussion and Analysis of Financial condition and results           of operations Report C.Business Overview Report D.Notes to Financial statements Report
##### Watch this video and then use the figure below to answer the question
Watch this video and then use the figure below to answer the questions. Part A Match each component of the electron transport chain with its description. Drag the terms on the left to the appropriate blanks on the right to complete the sentences.
##### For the conditions given in the previous question, the charge's actual trajectory is:
In the figure below, a magnetic field of 0.6 Tesla points into the page. A particle of charge $$-12 n C$$ and mass $$0.6 ? g$$ is shot into the field as shown in the figure with a velocity of $$0.1 \mathrm{~km} / \mathrm{s} .$$ What is the radius of the orbit (in meters)? (The radius is a positive quantity.) Be careful with the powers of 10. Hint: k=kilo, m=milli, ?=micro, $$n=$$ nano and the SI units for B-field, charge,...
##### Question 4.12 Solution(Mastering Physics Chapter 04: Force and Motion)
Part A The kinematic equation x = x0 + V0t + 1/2at2 can be used: Only with constant velocities. Only with constant forces. With variable accelerations. All of the preceding
##### Question 4.10 Solution(Mastering Physics Chapter 04: Force and Motion)
Part A A brick hits a glass window. The brick breaks the glass, so: The magnitude of the force of the brick on the glass is greater than the magnitude of the force of the glass on the brick. The magnitude of the force of the brick on the glass is equal to the magnitude of the force of the glass on the brick. The magnitude of the force of the brick on the glass is smaller than the magnitude...
##### Question 4.4 Solution(Mastering Physics Chapter 04: Force and Motion)
Part A If the net force on an object is zero, the object could: Have zero acceleration. Be at rest. Be in motion at a constant velocity. All of the preceding