![fatherbamboo](/avatars/46830.jpg)
fatherbamboo
08.01.2020 •
Mathematics
7people enter a race. there are 4 types of medals given as prizes for completing the race. the winner gets a platinum medal, the runner-up gets a gold medal, the next two racers each get a silver medal, and the last 3 racers all get bronze medals.
what is the number of different ways the medals can be awarded?
a) 7! /3! b) 7! /2! 3! c) 1*1*2! *3! d) 7*6*2! *3! e) 7*6*5*4
Solved
Show answers
More tips
- F Family and Home Protect Your Home or Apartment from Pesky Ants...
- O Other What is a Disk Emulsifier and How Does it Work?...
- H Health and Medicine How to Calm Your Nerves? Expert Tips That Actually Work...
- A Animals and plants 5 Tips for Taking Care of Yews to Keep Them Green and Beautiful...
- S Sport How to wrap boxing hand wraps? Everything you need to know!...
- F Food and Cooking 10 Reasons Why You Should Avoid Giving Re-Gifts: An Informative Guide...
- F Family and Home Tender Care for Your Parquet: Is it Possible to Clean Parquet?...
- S Style and Beauty How Are Eyelash Extensions Applied? All Your Questions Answered...
- F Food and Cooking 10 Tips for Proper Sushi Consumption...
- S Style and Beauty Learn how to tie a keffiyeh on your head like a pro...
Answers on questions: Mathematics
- M Mathematics Miranda has $60,000 in a savings account that earns 10 % annually.The interest is not compounded.How much interest will she earn in 4 months?...
- M Mathematics Soccer cleats cost $119.99. what would the cost be if you received the 35% discount and then the 10% discounts? is this 45% off the original price?...
- M Mathematics 3/4(1440) + 295.25 + (-33.50)...
- M Mathematics How do I convert (6,240°) to rectangular coordinates...
- M Mathematics Find the z-score that corresponds to a cumulative area of 0.4761...
- M Mathematics You might need: Calculator g(t) = -(t - 1)2 +5 What is the average rate of change of g over the interval -4...
- M Mathematics Convert -5i to polar form...
- M Mathematics Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options....
- M Mathematics Simon is having a birthday party, and each guest gets a bag of party favors. Each goody bag contains one of 7 different toy cars and one of 3 different toy trucks. Each...
- M Mathematics Which of these situations could be written as an equation with one variable? A Penny picked 35 apples, Ben picked 22 and Sam picked 17. They picked 74 apples all together....
Ответ:
b)
Step-by-step explanation:
The number of ways of awarding the medals is equal to the number of ways of choosing a winner, a runner up, the next two racers and the last 3 racers from our group of 7 people (the different positions of the racers).
To count this, we use the multiplication principle from combinatorics. It says that if there are A ways of doing something and B ways of doing another thing, there are A×B ways of doing both things.
First, there are 7 people and we have to choose 1 winner. This can be done in 7 ways. This person earns the platinum medal
After choosing the winner, 6 people remain. We have to choose 1 runner-up from this group, which can be done in 6 ways.
Now, 5 people remain. We have to choose 2 of them for the silver medal. Since the order between them doesn't matter (they get a silver medal regardless who was 3rd or 4th) the number of ways of doing this is equal to the binomial coefficient
.
3 people remain. They will be the last racers, so there is only 1 way of choosing them.
Using the multiplication principle, the number of ways of awarding the medals is![7(6)\frac{5!}{2!3!}=\frac{7(6)(5!)}{2!3!}=\frac{7!}{2!3!}](/tpl/images/0446/4413/7f251.png)
Ответ:
4,9,7,8
10,3,4,4
9,5,8,0
7,6,9,8
9,10,8,0
4,3,9,9
3,4,9,4
9,7,8,6
7,5,0,5
1,10,7,10
6,0,6,1