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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

erma4kov [3.2K]

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 that $n\ge h\ge i\ge j\ge k\ge m\ge 1$

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

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

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

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

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

Solved

6 0

2 years ago

The measure of anglerst can be represented by the expression (6x 12)°. three lines extend from point s. the space between lines

miv72 [106K]

Answer:

∠RST = 120°

Step-by-step explanation:

We assume the positions of the lines and angles will match the attached figure. The angle addition theorem gives a relation that can be solved for x, then for the value of angle RST.

∠RSU +∠UST = ∠RST

__

78° + (3x -12)° = (6x +12)° . . . . . substitute given values into the above

54 = 3x . . . . . . . . . . . . . . . . divide by °, subtract 3x+12

108 = 6x . . . . . . . . . . . multiply by 2

120° = (6x +12)° = ∠RST . . . . add 12, show units

The measure of angle RST is 120 degrees.

_____

Additional comment

Note that we don't actually need to know the value of x (18) in this problem. We only need to know the value of 6x.

7 0

1 year ago

State what additional information is required in order to know that the triangles are congruent for the reason given. If possibl

earnstyle [38]

Answer:

XY ≅ TU

Step-by-step explanation:

SAS = side- angle- side

It requires two sides and the included angle be congruent.

Given one congruent side and one congruent adjacent angle.

In addition to what is given we need the other side be congruent too:

XY ≅ TU

8 0

2 years ago

Read 2 more answers

Sarah completed about 85% of her school homework. Her friend Emily completed x percent homework more than Sarah. Which expressio

Ilia_Sergeevich [38]

Answer:

Step-by-step explanation:

85-x=100

85 represents sarah's hw

x represent Emily's hw

100 represents total completion

8 0

2 years ago

Read 2 more answers

Which is an appropriate estimate

saveliy_v [14]

Answer:

40

Step-by-step explanation:

This answer is the closest when it comes to 3,844 divided by 75.

6 0

2 years ago

Read 2 more answers