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
PSYCHO15rus [73]
3 years ago
13

Consider a city whose streets are laid out as a grid. Streets run north-south or east-west. A visitor is dropped off by a cab at

a certain intersection and would like to visit a museum that is 6 blocks to the east and 3 blocks to the north of his current location. The visitor always takes a direct path and never travels west or south in the course of his walk. How many distinct paths are there for the visitor to walk to the museum
Mathematics
1 answer:
Ann [662]3 years ago
3 0

Answer:

84 possible paths

Step-by-step explanation:

Given

N =3 --- 3 blocks north

E = 6 --- 6 blocks east

Required

Number of distinct path

To solve this question, we make use of the following formula

^{m+n}C_n \ =\ ^{m+n}C_m

The above formula implies that;

On a single path, there is a total of m + n steps to get to a particular position, where each path is either in m direction or n direction.

In this case:

m = 3

n = 6

So, we have:

^{m + n}C_n = ^{3+6}C_6

^{m + n}C_n = ^9C_6

Apply combination formula

^{m + n}C_n = \frac{9!}{(9-6)!6!}

^{m + n}C_n = \frac{9!}{3!*6!}

Expand the numerator

^{m + n}C_n = \frac{9*8*7*6!}{3!*6!}

^{m + n}C_n = \frac{9*8*7}{3!}

Expand the denominator

^{m + n}C_n = \frac{9*8*7}{3*2*1}

^{m + n}C_n = \frac{504}{6}

^{m + n}C_n = 84

<em>Hence, there are 84 possible paths</em>

<em></em>^{m + n}C_m<em> will also give the same result</em>

You might be interested in
What is the slope of the line whose equation is -3x y=12?
stepan [7]
-3x+y=12
y=3x + 12
slope=3
8 0
3 years ago
Acellus
USPshnik [31]

Answer:

<6

Step-by-step explanation:

Corresponding angles have the same matching corner when a transversal line crosses tow straight lines.

Thus, in the diagram given, the angle that has the same matching corner with <2 is the angle that corresponds to <2.

<6 has the same matching corner with <2.

Therefore, <6 corresponds with <2

7 0
3 years ago
The town of lantana needs 14,000 for a new playground. Lantana elementary school raised 5,258, Lantana middle school raised 2834
Nutka1998 [239]
Lantana needs $1776 to reach its goal of $14000
5 0
3 years ago
One hundred times the quantity five plus three
Maru [420]
Five-5

three-3

"the quantity five plus three" (5 + 3) 

"one hundred times the quantity ..." means  100 (5 + 3)   

now just solve 100(5+3) 

solve the parentheses first (5+3) = 8

Now you are left with 100(8) or 100*8

when you solve your answer is 800
3 0
3 years ago
PLS HELP ME solve the system of equations <br> all I need is to find x,y and z
ale4655 [162]

(x,y,z)=(-4,-2,-5)

I added some images for explanation

7 0
3 years ago
Other questions:
  • Help me with 4 5 6 7 8 9 plzz
    13·1 answer
  • g a local tv network estimates that the avergae number of viewers during primetime on weekdays is normalling distributed with a
    5·1 answer
  • Solve for X.<br> −68 &lt; 8x − 4 &lt; −36
    11·2 answers
  • At dee dee's dinette the probability that a customer orders coffee is 0.60, the probability that a customer orders pie is 0.35,
    11·1 answer
  • If ΔABC is reflected across the y-axis, what are the resulting coordinates for points A', B', and C'
    6·1 answer
  • Can a number be both rational and irrational
    15·2 answers
  • Ella is 12.537 miles from her house which shows the value of 12.537 rounded to the nearest tenth and nearest hundredths F 12.6,
    15·1 answer
  • What is the product of z and 5
    6·1 answer
  • 1.1.2<br>Calculate the amount of VAT payable on a coffee mug that costs R75.90<br>(VAT exclusive)​
    7·1 answer
  • Is 6 cups more or 2 pints ?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!