How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?

60 different numbers can be formed

Step-by-step explanation:

Note that we have 5 different digits, and we must select 3 of them. They should not be repeated

The order of selection is important in this case, because the number 532 is not the same as the number 235.

So we have a permutations problem, where we have a set of n elements and we want to choose r from them.

Then we define the permutacion as:

In this case note that n=5 because there are 5 elements in the set.

r = 3 because we combine the elements to form three-digit numbers

Then:

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.