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
Ming is mowing a lawn that is 12 feet wide and 25 feet long.
leva [86]

Answer:

300!

Step-by-step explanation:

Because square feet is area and area is length (25) and width (12)

5 0
2 years ago
Read 2 more answers
What is the equation in slope-intercept form of a line that is parallel to y=2x+5 and passes through the point (2, 8)?
trapecia [35]

Answer:

Step-by-step explanation:

y - 8 = 2(x - 2)

y - 8 = 2x - 4

y = 2x + 4

5 0
3 years ago
Read 2 more answers
During a spring clearance sale, Sears advertise 1/4 off the list of Model II microwave ovens and an additional 1/5 off the sale
ozzi

Answer:

$ 75.

Step-by-step explanation:

From the information above,

List price of model II = $240

Sale price of the clearance sale is 1/4 off the list price of Model II microwave oven and additional 1/5 of the sale price for oven that are scratched and dented.

Therefore,

Let the sale price be X,

= (1/4)*(list price) + (1/5)*X

X = (1/4)*(240) + (1/5)*X

X = 60 + (1/5)X

Solving for X,

X - (1/5)X = 60

(4/5)X = 60

X = (60*5)/4

= $75.

4 0
3 years ago
Help, help!!! Please:)
andrew-mc [135]

Answer: b

Step-by-step explanation:

3 0
3 years ago
How do you;<br><br> Write a word problem that can be solved by using 2 x 5 / 5?
ale4655 [162]
Marcus had 5 horses and Rachel had 5 times more. She had to divide them into 5 stalls. How many are in each stall?
4 0
3 years ago
Other questions:
  • Find the values of x,y,z. This diagram is not a scale.
    11·2 answers
  • There are 75 students in a speech contest. Yesterday, 2/5 of them gave their speeches. Today, 1/3
    8·1 answer
  • If you need more than 60% of the students surveyed to like your product how many out of 500 would you have to survey
    7·1 answer
  • I need resolve this 5+4-5+3*8/2=???
    6·2 answers
  • 3/10 estimated plz help ASAP
    15·1 answer
  • BRAINLIEST <br><br> which expressions are polynomials select each correct answers
    14·1 answer
  • Monique rolls a six-sided number cube labeled 1 to 6.
    8·2 answers
  • In Minnesota, the current temperature is 35.7​ o​ F and is dropping 2.5​ o​ F every day. Greenland’s temperature is 25.2​ o​ F a
    5·1 answer
  • Write a unit rate for the situation.<br><br> 228 students in 12 classes
    8·2 answers
  • Help quick Please!...........................................
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!