Jamie takes part in a quiz competition. she is asked to name the total number of combinations that the bits 1 and 0 will have in a byte. what will be her answer?
a. 256 or 28 different combinations
b. 257 or 28 different combinations
c. 255 or 28 different combinations
d. 255 or 29 different combinations

A. or different combinations

Explanation:

First of all, we have two possible digits or options to choose from, bits 1 and 0. From the question, we know that every combination should form a byte. So, we have to choose eight times (eight bits). For example, a combination could be [ 10001000 ]  another could be [ 00011000 ].

As you can see the order of the digits makes to change the combination. So, byte [ 10000000 ] is different than byte [ 00000001 ]. In the right math language order matter and this is called permutation.  We can say that a permutation is a combinations where order matter.

For a permutation like this, where we can repeat digits, it is possible to calculate the total of permutations by using the formula, × ×

Where:

is the number of digits or options to choose from

is the number of digits we choose to make a permutation

From the problem we get that:  

(bits 1 and 0)

(a permutation should form a byte)  

let's replace all values into the formula :

× ×  

256 permutations (combinations where order matter)

We can conclude that the total number of combinations that the bits 1 and 0 will have in a byte are A. or different combinations

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