The martian colonies elect their government through a lottery. there are100,000 people living on mars, and every year, a council of 99 co-equalleaders is randomly selected from the population. in how many ways canthe leadership be elected? give your answer in terms of permutations orcombinations and explain your choice. you do not have to evaluate.

The answer is a 100,000-choose-99 (a combination.)

.

Step-by-step explanation:

A combination or equivalently gives the number of ways to choose out of elements.

A permutation also gives the number of ways to choose out of elements. On top of that, it accounts for the order of the elements. Two elements in different order counts twice in a permutation, but only once in a combination.

The question emphasize that the council members are "co-equal." That implies that the order of the members don't really matter. Hence a combination with and would be a more suitable choice.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .