Question

In: Advanced Math

What is the number of ordered sequences of length k where each digit is taken from...

What is the number of ordered sequences of length k where each digit is
taken from a set of size n?

What is the number of ordered sequences of length k where each digit is
taken from a set of size n without repetition?

What is the number of subsets of size k of a set of size n?

Solutions

Expert Solution

FIRST PART:

There are choices for each of the places.

Therefore, number of ordered sequences of length where each digit is taken from a set of size

SECOND PART:

Since repetition is not allowed, the first place has choices, the second place has remaining choices, and so on.

Finally, the last place has choices.

Therefore, number of ordered sequences of length where each digit is taken from a set of size without repetition

THIRD PART:

Finding number of subsets of size is same as finding number of unordered sequences of length where each digit is taken from a set of size without repetition.

By previous calculations, number of such ordered sequences

But order of elements does not matter in a set.

i.e., for every subset , any permutation is also the same subset.

There are such permutations for every set.

So, number of such unordered sequences

i.e., number of subsets of size

Colby Messinger answered 3 weeks ago

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