Alexa is choosing a number for her new combination lock. She can use three differents digits from 0 to 9. How many arrangements are there?
I think 3 ways 9 divided by 3 equals 3 .......
170
To determine the number of arrangements Alexa can make for her combination lock using three different digits from 0 to 9, we can use the concept of permutations.
Permutations refer to the different ways in which objects can be arranged. In this case, Alexa has 10 digits (0 to 9) to choose from, and she can use three different digits. We can calculate the number of arrangements using the formula for permutations:
nPr = (n!)/(n-r)!
Where n is the total number of objects from which we can choose, and r is the number of objects we are choosing.
In this case, n = 10 (10 digits available) and r = 3 (Alexa needs to choose three different digits). Plugging in the values, we get:
10P3 = (10!)/(10-3)!
= (10!)/(7!)
To simplify the calculation, we can expand the factorials:
10! = 10 x 9 x 8 x 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
Substituting these values in the formula:
10P3 = (10 x 9 x 8 x 7!)/(7 x 6 x 5 x 4 x 3 x 2 x 1)
Now, we can cancel out the common factor of 7!:
10P3 = (10 x 9 x 8)/(1)
Therefore, there are 720 different arrangements Alexa can make for her combination lock using three different digits from 0 to 9.