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]

Guest Nov 13, 2019

#2**0 **

Oh and for the last question, please explain thoroughly, with explanations to your method.

Guest Nov 13, 2019

#3**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.

wonderman Nov 13, 2019

#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.

chrissy Nov 13, 2019