1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
AURORKA [14]
3 years ago
12

The price of a European tour includes stopovers at five cities to be selected from 15 cities. In how many ways can a traveler pl

an such a tour if the traveler can only choose the five cities (the order is determined by the travel company).
Mathematics
1 answer:
xeze [42]3 years ago
4 0

Answer:

The traveler can plan such a tour in 3003 ways.

Step-by-step explanation:

The order that the cities are chosen is not important, since it is chosen by the company and not by the traveler. So we use the combinations formula to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this problem, we have that:

Combinations of 5 cities from a set of 15. So

C_{15,5} = \frac{15!}{5!10!} = 3003

The traveler can plan such a tour in 3003 ways.

You might be interested in
For a certain​ candy, 15​% of the pieces are​ yellow, 1010​% are​ red, 2020​% are​ blue, 55​% are​ green, and the rest are brown
MatroZZZ [7]
A) the probability it is brown would be 50%; the probability it is yellow or blue would be 35%; the probability it is not green is 95%; the probability it is striped is 0%.
B) the probability of all brown would be 12.5%; the probability that the third one is the first red one drawn is 8.1%; the probability that none are yellow is 61.4%; the probability that at least one is green is 14.3%.

Explanation:
A) The probability that it is brown is the percentage of brown we have.  Brown is not listed, so we subtract what we are given from 100%:
100-(15+10+20+5) = 100-(50) = 50%.  The probability that one drawn is yellow or blue would be the two percentages added together:  15+20 = 35%.  The probability that it is not green would be the percentage of green subtracted from 100:  100-5=95%.  Since there are no striped candies listed, the probability is 0%.
B) Since we have an infinite supply of candy, we will treat these as independent events.  All 3 being brown is found by taking the probability that one is brown and multiplying it 3 times:
0.5*0.5*0.5 = 0.125 = 12.5%.  
To find the probability that the first one that is red is the third one drawn, we take the probability that it is NOT red, 100-10 = 90% = 0.9, for the first two, and the probability that it IS red, 10% = 0.1, for the last:
0.9*0.9*0.1 = 0.081 = 8.1%.

The probability that none are yellow is found by raising the probability that the first one is not yellow, 100-15=85%=0.85, to the third power:

0.85^3 = 0.614 = 61.4%.

The probability that at least one is green is computed by subtracting 1-(probability of no green).  We first find the probability that all three are NOT green:
0.95^3 = 0.857375
1-0.857375 = 0.143 = 14.3%.
3 0
3 years ago
3^{x^{2}}=2^{\log_{3}2}\\find\:{3}^{x}​
Rashid [163]

Answer:

b r u h what

Step-by-step explanation:

6 0
2 years ago
HELP!!!! I WILL GIVE BRAINLIEST TO THE FIRST ANSWER!!!!!!!
aleksklad [387]
I would say c. I’m not sure if I’m right if I’m not sorry but good luck
3 0
3 years ago
Rewrite the equation y – 4x = –9 in slope-intercept form.
Luda [366]

Answer:

The answer should be A. Y= -4x -9

4 0
2 years ago
Find the slope and the y-intercept of the line.<br><br><br> 5x + 8y = 31
Sunny_sXe [5.5K]

Step-by-step explanation:

1.) Move the 5 to the other side of the equation

8y = -5x + 31

2.)

Divide by 8

y= .625x + 3.8

8 0
1 year ago
Read 2 more answers
Other questions:
  • Assume that in january 2013, the average house price in a particular area was $288,400. in january 2002, the average price was $
    13·1 answer
  • Help is appreciated. Easy I just am always confused
    8·1 answer
  • 7m plus 8 equals 71 <br> How do u solve
    13·1 answer
  • -2x + 10 +4x=70 (what is X?)
    12·2 answers
  • What is the sum of the first 14 terms of the sequence an = 6n -12
    14·1 answer
  • One landscaper works 1.5 times as fast as another landscaper. Find their individual times if it takes 9 hours working together t
    13·1 answer
  • A cylinder has a radius of 14m and height of 6m. What is the exact volume of the cylinder?
    5·2 answers
  • Whoever responds first will get marked Best.
    7·1 answer
  • The corporate team building ecent will cost $6 if it has 3 attendees. if there are 8 attendees how much will the corporate team
    13·1 answer
  • I need help with numbers 17 and 18.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!