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