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
Alla [95]
2 years ago
12

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

e written in increasing order but are not necessarily distinct? In other words, how many 5-tuples of integers (h, i, j, k, m) are there with 1 ≤ h ≤ i ≤ j ≤ k ≤ m ≤ n? As in Example 9.6.3, you can represent any ordered 5-tuple of integers (h, i, j, k, m) with 1 ≤ h ≤ i ≤ j ≤ k ≤ m ≤ n as a string of n − 1 vertical bars and 5 crosses, with the position of crosses indicating which 5 integers from 1 to n are included in the 5-tuple. Thus, the number of 5-tuples is the same as the number of strings of n+4 vertical bars and 5 crosses, which is n(n+1)(n+2)(n+3)(n+4) 120​ .
Mathematics
1 answer:
erma4kov [3.2K]2 years ago
6 0

Answer:

\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}

Step-by-step explanation:

Given

5 tuples implies that:

n = 5

(h,i,j,k,m) implies that:

r = 5

Required

How many 5-tuples of integers (h, i, j, k,m) are there such thatn\ge h\ge i\ge j\ge k\ge m\ge 1

From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.

Also considering that repetition is allowed:  This implies that, a number can be repeated in more than 1 location

So, there are n + 4 items to make selection from

The selection becomes:

^{n}C_r => ^{n + 4}C_5

^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}

^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}

Expand the numerator

^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}

<u><em>Solved</em></u>

You might be interested in
Find the greatest common factor of 15x 2 y 3 and -20x 3 yz.
vekshin1
Multiply the GCF of the numerical part 3 and the GCF of the variable part x^2y to get 
3x^2y. 
7 0
2 years ago
Read 2 more answers
If it is a 20% tip, is $95.40. What was the amount of the bill before the tip?
labwork [276]

Answer:

$114.48

Step-by-step explanation:

7 0
2 years ago
Find the greatest common factor of 20, 70, and 50.
posledela

Answer:

=10

Step-by-step explanation:

because 20÷10=2

70÷10=7

50÷10=5

7 0
3 years ago
I WILL MAKE BRAINIEST
WINSTONCH [101]

Answer:

Lol this is on khan Academy isn’t it and the answer is 5 miles to 1 hour so 5:1

Step-by-step explanation:

6 0
2 years ago
Find the value of x <br> A. 90.3 <br> B. 13.4<br> C. 9.5 <br> D. 14.2
nevsk [136]

Answer:

..

<( (>GOOD LUCK CHARLIE

/ \

_ _

5 0
3 years ago
Other questions:
  • HURRY!!! PLEASE HELP WITH QUESTIONS!!!! WILL MAKE BRAINIEST ANSWER!!!!
    10·2 answers
  • A clothing shop is offering a 12 percent discount for senior citizens. Which equation represents the discount price?
    11·2 answers
  • Find (f o g)(1) for the following function<br> f(2)=-10 and g(1)=2
    5·1 answer
  • Use the discriminant to decide how many solutions the given equation will have. Show all work for credit. 6x^2-2x=3
    6·1 answer
  • I need help!!!! :))))
    13·1 answer
  • Is n=10 a solution to this equation? n/2 + n = 10
    15·1 answer
  • the length of a rectangle is 10 ft more than the width. if the perimeter is 64 feet then what is the length of the rectangle in
    14·1 answer
  • Select each situation that can represent a proportional relationship
    8·2 answers
  • Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below/attached
    7·2 answers
  • Pls help ill give brainliest to the person WHO GETS IT RIGHT
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!