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Thanks for adding to my growing knowledge of new math!

-1 choose 1 is impossible, it is not -1.

Anything choose 0 is 1, Anything choose 1 is the number i.e. 1 choose 1 is 1, 2 choose 1 is 2, 3 choose 1 is 3 and so on. You can't use negative numbers is combinatorics.

I belive it would be

0 choose 0 = 1

1 choose 1 = 1

So then whats..

0 choose 0

1 choose 1

-1 choose 1

To calculate the number of happening of an event, N chooses K tool is used. N is the sum of data and K is the number that we chose from the sum of data.

The formula for N choose K formula is

:\(C(n, k)= n!/[k!(n-k)!] \)Where,
n is the total number
k is the number of selected item

Solved Examples

Question 1: How many ways to draw exactly 6 cards from a pack of 10 cards?

Solution:

From the question, it is clear that,
N = 10
N = 6

So the formula for n choose k is,\(C(n, k)= n!/[k!(n-k)!] 610C=10!6!(10−6)!=362880017280 \)= 210

So, there are 210 ways of drawing 6 cards in a pack of 10.

This formula and topic is very useful in solving various types of problems I recommend that you you practice this topic until you feel like you can solve and N choose K question.

Here to help

:D

Here's my best shot

A.  AB and CD  must be the same length and have the same slope

B. 

AB  = sqrt [ 3 - 0)^2  + (4-0)^2 ] =  sqrt ( 3^2 + 4^2)  = sqrt (25)  = 5

CD  = sqrt [ (4 - 7)^2 + (7-3)^2 ]  = sqrt [ (-3)^2 + 4^2]  = sqrt (25) = 5

Slope of AB  =  [ 4-0] / [0 - 3]  = -4/3

Slope of CD  = [7 - 3 ] / [4 - 7] = -4/3

C. We only need to show that AD and BC  = 5   (they are)

D.  If we can prove that  AD = BC  =5    and  AD is perpendicular to AB  and BC is perpendicular to CD.....we will have a square   [  these are true, as well ]

CONVERT 1/7 TO BASE 9 =0.12512512512512..._9

To convert 1/7 to base 9, just multiply: 1/7 x 9 =1 + (2/7 x 9)

                                                                                     =12 + (4/7 x 9)

                                                                                     =125 + (1/7 x 9)..then it repeats

                                                                                     =125125125125.....in base 9

Hey, GM!!!

Note that if   QR :RS  = 1 : 2....then  (think about this)....QR  must just be 1 / [ 1 + 2 ]  = 1/3  of the  total length of  QS

So  numerator  = 1

And denominator  = 3

Here's the way to find R

( -9 + (1/3) (9 - - 9) , 8 + (1/3) ( -4 - 8) )  =

(-9 + (1/3)(18) , 8 + (1/3) (-12) ) =

( -9 + 6, 8 - 4)   =

(-3, 4)  = R

See this image to verify this :

Thanks Alan :)

cos B  =   x  / r

r  = √ [ (-7)^2  + (2√3)^2 ]  =  √ [ 49+ 12]  = √61

So

cos B  =  -7  /√61   =   -7√61/ 61

605 = 5 * 11^2. Since 11 is not a single digit, that means that GOD is 605 not G * O * D = 605. In that case, can you please clarify the functions of adjacent letters. And what does the space mean in "ADAM AND EVE". Also, does ADAM mean A * D * A * M, or does it mean a 4-digit number ADAM?

11:15

thanks so much!!!

We have a 30-60-90 right triangle

The hypotenuse =  2/√3  times the side opposite the 60°  angle

So

9 * 2  /√3  =   18/√3  =   18√3 / 3   =   6√3

You are correct   !!!

I think   "14"  might be  " 1 / 4"

If so

20  /[ 1/4]   =

[20/1] * [ 4/1]  =   80 / 1   =  80  portions

LOL!!!....yeah, Melody....I forgot to thank Andre!!!!

The "formula" is

A  =  P  ( 1 + r/n) ^(y*n)

Where

A  = the amt we are looking for

P = the beginning amt

r = the interset rate expressed as a decimal

n = the number of compoundings per year

y = the number of years

So we have

A = 5000 ( 1 + .08/4)^(10*4) ≈ $11040.20

Thanks very much Alan.  

Thanks to admin for the fix too.   

THX, alan   !!!!!

Thanks, alan   !!!

Here's an easy way to remember this......

r  = asin (n θ)

or

r  = acos(n θ)

When n is odd.....the number  of petals  =  n

When n is even.....the number of petals  = 2n

So 

r = 4sin (3 θ)    has  n  odd....so....it will have n =  3 petals