A telecommunications cable contains 8 wires that are colour coded. there are 8 different colours. how many different ways could these colours be arranged.
A. 40 320
B. 5 040
C. 256
D. 224
Assume they are position dependent.
The first wire has 8 ways, the second has 7, so there are 56 ways. Continue this way down to the last wire (1 way). Multiply them together and see that the product matches one of the answers.
To determine the number of different ways the 8 colors can be arranged, we can use the concept of permutations.
In this case, since there are 8 colors and 8 wires, we want to find the number of permutations of the 8 colors taken all at once.
The formula to calculate permutations is n!, where n is the total number of items. "!" represents the factorial, which means multiplying a number by all the positive integers less than it down to 1.
So, in this case, we need to calculate 8!.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Therefore, the correct answer is A. 40,320 different ways.