DNA Oligonucleotide probe designing someone help me to learn

 
My professor gave me three amino acid sequence and using the codon table he asked me to design a set of DNA oligonucleotide probe which can be used to detect in a library. He also asked me to find out the preferable oligonucleotide probes used to screen a library.
 
The peptide sequence given by him is
(a)        H-C-W-K-M
5¢- CAU – UGU – UGG – AAA – AUG - 3¢
            OR
5¢- CAC – UGC – UGG – AAG – AUG - 3¢
 
In this way I also have
(b)       R-S-L-L-S
(c)        D-A-Q-W-Y
 Similarly I got sequence for R-S-L-L-S and those sequences are
5¢- CGU – UCU –CUU—CUU – AGU- 3¢
 
5¢- CGC – UCC –CUC—CUC– AGC- 3¢
Like this two more combinations are also possible,
 
Similarly I have 4 possible sequences for D-A-Q-W-Y
Keeping this information how to design a oligonucleotide probe as well how to choose the preferable probe which can be used to screen a library. Kindly explain me from the basics so then I can understand the concept well. Please help me.