(a) There are $n$ chairs in a row. Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.

(b) There are 10 chairs in a circle, labelled from 1 to 10. Find the number of ways of choosing 3 of these chairs, so that no two chosen chairs are adjacent.

(c) There are $n$ chairs in a circle, labelled from 1 to $n.$ Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.

Evaluate the following expression 1/3^2

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

The scatterplot below shows the number of hours that students read weekly and the number of hours that they spend on chores weekly. which statement about the scatterplot is true?