# Make up a counting problem for your classmates to solve. It can be one that requires the fundamental counting principle, a permutation, or a combination. Do not solve it yourself. Find all the...

- Make up a counting problem for your classmates to solve. It can be one that requires the fundamental counting principle, a permutation, or a combination. Do not solve it yourself.

- Find all the subsets of a set.
- Count the number of elements in a set.
- Solve counting problems using the multiplication principle.
- Solve counting problems using permutations involving n distinct objects.
- Solve counting problems using combinations.
- Solve counting problems using permutations involving n non-distinct objects.
- Construct probability models.
- Compute probabilities of equally likely outcomes.
- Find probabilities of the union of two events.
- Use the complement rule to find probabilities.

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### 1 Answer

A section of one strand of DNA consists of 100 nucleotides. The nucleotides are one of guanine(G), adenine(A), thymine(T), or cytosine(C).

How many different strands are possible?

** Each position has 4 possibilities so the total is `4^(100) `

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How many different 3 letter "words" can be formed by the letters in your state/county/nation? (e.g. how many different 3 letter words can be formed by the letters in Illinois?)

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How many different sets can you form using the elements a,b,c no more than once each?

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