In mathematics, the study of combinations refers to the number of ways one can s

Question

In mathematics, the study of combinations refers to the number of ways one can select items from a group disregarding order; the study of permutations refers to the number of ways one can permute, or arrange, items into a sequence. Given that each entry in a binary string must be either a 1 or a 0, what is the total number of addresses that can be encoded using a 32-bit binary string? Is this a combination or permutation problem? Justify your answer.

In IPv6, 128 bit, binary strings are used for addressing. How many addresses can be encoded using 128 bits? Is this a combination or permutation problem? Justify your answer.

In IPv4, how many addresses contain exactly eight 1s?

Explanation / Answer

1.) It is a permutation problem as we are not selecting anything. Since each place can be filled by either a 0 or 1, for each bit, we have 2 options. So, total number of address that can be encoded using a 32-bit string is 2^32.

2.) Similarly, it is a permutation problem as we are not selecting anything. Therefore, using 128 bits, we can encode 2^128 addresses.

3.) In order to get exactly eight 1's, we will have 32C8 addresses.

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