# 11: Summary The Law of Combining says: If you want to count the possible combinations of ONE PICK from set 1 and ONE PICK from set 2, you can just multiply the size of set 1 by the size of set 2.

Or simply,

Ntot = N1 x  N2

If you are picking multiple times from the same set, you can use an exponent:

Ntot = (Nset ) # picks

Using the Law of Combining will often get you some very big numbers, which might be better expressed using:

• scientific notation, or
• logs

Nucleotides form a 4-letter alphabet and the same Law of Combining applies to them as well.

Although BLAST contains a huge number of nucleotide sequences, it is tiny compared to the number of POSSIBLE nucleotide sequences.

In order to compare sizes, you need to divide. For scientific notation, this means

“Divide the numbers (preceding the power of 10) and subtract the powers”.

## Learning Outcomes

Now that you have worked through this module, you should be able to:

• Use the law of combining to count the number of possible combinations of items from one or more sets.
• Apply the law of combining to deduce the number of nucleotide sequences and amino acid sequences in a given context.
• Multiply and divide numbers given in scientific notation.
• Deduce the average number of nucleotide sequences per amino acid sequence.
• Deduce the likelihood of a particular nucleotide sequence being catalogued in BLAST.

If you want a printer-friendly version of this module, you can find it here in a PDF  document. This printer-friendly version should be used only to review, as it does not contain any of the interactive material, and only a skeletal version of problems solved in the module.