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
Gnoma [55]
1 year ago
10

Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

simplest form.

Mathematics
1 answer:
umka2103 [35]1 year ago
7 0

Solution:

The permutation formula is expressed as

\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\  \end{gathered}

The combination formula is expressed as

\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\  \\  \end{gathered}

where

\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}

Given that 6 objects are taken at a time from 8, this implies that

\begin{gathered} n=8 \\ r=6 \end{gathered}

Thus,

Number of permuations:

\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}

Number of combinations:

\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}

Hence, there are 28 combinations and 20160 permutations.

You might be interested in
Please help me on this!
Tanya [424]
Answer: A. 4.
Explanation: solving graphically
6 0
1 year ago
In order to make an A on her project, Sarah needs at least 160 points. She has already turned in part of her work and has been g
antoniya [11.8K]

to get an A, she needs >=160 points and she already has 125 points

let 'x' be the number of points on the last part of her project then

125 + x >= 160

x >= 160 - 125

x >= 35

Sarah needs at least 35 points on the last part of her project.

8 0
3 years ago
Read 2 more answers
Harry and Selma start driving from the same location. Harry drives 42 miles north while Selma drives 144 miles east. How far apa
weqwewe [10]
186 Miles. Just add 144+42=186 Miles.
7 0
3 years ago
If sin theta is negative and cot theta is positive, in which quadrant does theta terminate?
krok68 [10]

All you need to know is that:

  • In the first quadrant, both coordinates are positive
  • In the second quadrant, x is negative and y is positive
  • In the third quadrant, both coordinates are negative
  • In the fourth quadrant, x is positive and y is negative
  • The sine is the y coordinate of the points on the unit circle
  • The cosine is the x coordinate of the points on the unit circle
  • The cotangent function is defined as the ration between the cosine and the sine of an angle.

So, if sin theta is negative and cot theta is positive, you're saying that you're looking at a point with negative y coordinate and such that

\dfrac{\cos(\theta)}{\sin(\theta)}>0

The ratio of two numbers is positive if and only if they have the same sign, so the cosine must by negative as well.

Saying that an angle has negative sine and cosine is the same as saying that the angle identifies a point on the unit circle where both x and y coordinates are negative.

So, if you look at the bullet list at the beginning, you'll see that the point is in the third quadrant.

8 0
3 years ago
I'm thinking of a ten-digit integer whose digits are all distinct. It happens that the number formed by the first n of them is d
PIT_PIT [208]
The problem here takes a brilliant mind to answer this. This problem can easily be answered using programming because we can not then and there push all the possibilities using paper and pen.
The answer is 3816547290. 
Trying all the possibilities starting form 1000000080 (we are sure that the last number should be 0). Then traversing that number until 9999999990. Each traverse, check the number if its divisible to n, so on and so forth.
3 0
3 years ago
Other questions:
  • In a box of 25 switches, 3 are defective. what is the probability of randomly selecting a switch that is not defective? enter yo
    10·1 answer
  • How to simplify 6x^2y^-3/x^-5
    10·1 answer
  • Neveah has created the function f(x) =the quantity of 2x plus 4, divided by 3 to represent the growth of her hair, where x repre
    10·1 answer
  • tickets at a particular movie theatre have different rates for adults and children. on a friday the theatre sold 4 adult tickets
    10·1 answer
  • 100 points people please help asap!
    7·1 answer
  • PLEASE HELP!! Using the SAS Congruence Theorem
    10·2 answers
  • A cube has a volume of 8 cubic inches. what is the length of each edge of the cube?
    13·2 answers
  • In 2005, Lee began working as a nurse anesthetist with a taxable income of $119,000. The Medicare tax was 1.45% and the Social S
    15·1 answer
  • I need help I can’t cuaet understand this
    12·1 answer
  • A box of 100 sanitizing wipes costs 12$.How much does one wipe cost?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!