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I need these questions bad. Just for clarification incase the asy codes don't work, those are supposed to be asymptote.

 

a)Find the number of 10-digit numbers where the sum of the digits is divisible by 5.

We say that a quadrilateral is a bow-tie if two of the sides cross each other. An example is shown below.
[asy]
unitsize(2 cm);

int i;
pair[] A;

for (i = 0; i <= 6; ++i) {
A[i] = dir(90 + 360/7*i);
dot(A[i]);
}

draw(A[1]--A[5]--A[6]--A[2]--cycle,red);
draw(Circle((0,0),1));
[/asy]

Seven different points are chosen on a circle. We draw all  chords that connect two of these points. Four of these 21 chords are selected at random. What is the probability that the four chords form a bow-tie quadrilateral?

 

c)I have a bag with 5 pennies and 6 nickels. I draw coins out one at a time at random. What is the probability that after 4 draws I have removed no more than 2 pennies from the bag?

 

d)

Find the number of ways of arranging the numbers 1,2,3...12 in a 3 by 4 array (with three rows and four columns), so that the sum of the numbers in each column is divisible by 3.

[asy]
unitsize(0.6 cm);

draw((0,0)--(4,0));
draw((0,1)--(4,1));
draw((0,2)--(4,2));
draw((0,3)--(4,3));
draw((0,0)--(0,3));
draw((1,0)--(1,3));
draw((2,0)--(2,3));
draw((3,0)--(3,3));
draw((4,0)--(4,3));
[/asy]
 

 Nov 13, 2019
 #1
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0

yup. okay. the asy codes don't work

sorry

 Nov 13, 2019
 #2
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Oh and for the last question, please explain thoroughly, with explanations to your method.

 Nov 13, 2019
 #3
avatar+117 
0

Please do not post solutions to these problems!  These are active homework problems.

 

To the original poster: I realize that homework may be challenging. If you wish to receive some help from the staff or other students, I encourage you to use the resources that the online classes provide, such as the Message Board.  Thanks.

 Nov 13, 2019
edited by wonderman  Nov 13, 2019
 #4
avatar+4 
+1

yup. these are AoPS problems. you can give up, message board, etc, or what I sometimes do is ask a math teacher at school. however, to process asymptote into images, go to the AoPS provided https://artofproblemsolving.com/texer/ and paste in the asymptote code. then, click "Render as Image" and you'll get a handy-dandy image that you can throw around.

 Nov 13, 2019

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