Suppose we want to choose for letters without replacement from 18 distant lovers how many ways can this be done if the order of the choices does not matter

This can be done in 3,060 ways.

Step-by-step explanation:

Letters are chosen without replacement, and the order does not matter, which means that the combinations formula is used.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:

Four letters from a set of 18. So

This can be done in 3,060 ways.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6