Question

in how many ways can you create a two-element set where each element in the set is an positive integer less than 110?

Answer 1

To create a two-element set where each element is a positive integer less than 110, there are 5985 different ways to do so.

Step-by-step explanation:

To create a two-element set where each element is a positive integer less than 110, we need to choose two numbers from the set of positive integers less than 110. The number of ways to do this can be found using the concept of combinations. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of elements and r is the number of elements we want to choose. In this case, n = 110 and r = 2. Plugging these values into the formula, we have 110C2 = 110! / (2! * (110-2)!), which simplifies to (110 * 109) / (2 * 1) = 5985.

Answer 2

There are 5904 ways to create a two-element set where each element in the set is a positive integer less than 110.

Step-by-step explanation:

To create a two-element set where each element is a positive integer less than 110, we need to choose two numbers from the set of positive integers less than 110.

The number of ways to do this is given by the combination formula, which is nCr = n! / (r! * (n-r)!), where n is the total number of elements and r is the number of elements to choose.

In this case, n = 109 (since the maximum positive integer less than 110 is 109) and r = 2. So the number of ways to create the set is:

nCr = 109! / (2! * (109-2)!)

= 109! / (2! * 107!)

= (109 * 108 * 107!) / (2 * 1 * 107!)

= (109 * 108) / (2 * 1)

= 5904

Therefore, there are 5904 ways to create a two-element set where each element in the set is a positive integer less than 110.