purpose of symbol ^
 

command to get the count of filenames start with "Foo" and end with an odd digit is:
ls -1 | grep '^Foo.*[13579]' | wc -l

what is the purpose of '-1' , '^', and '.' ?
will this command work if i don't put any one of these symbol?

The -1 argument to ls lists one file per line. For the rest. you need an understanding of how regular expressions (regexps) work, which is not necessarily that easy. Basically the ^ is negation or beginning of the line, depending on how its used in the regexp. In your case, it's the beginning of the line, so it's telling grep to match everything that starts with the pattern. The . is a single character wildcard. Combined with * the multi character wildcard, it basically says match everything. The command will still "work" if you change things, but it will match different patterns, so the resukts won't be the same. Read a tutorial on regexps for more info, they're way too complicated to explain in a forum post.

Ok. Thank you...

More info:

'ls -1' is used because you want to count files. If you used plain old 'ls' then you wouldn't get one file per line, so you couldn't pipe the output to the 'wc' command and tell it to count lines.

For the pattern '^Foo.*[13579]':

^Foo matches any line that starts with 'Foo' - the ^ means "start of the line" in this case

The single period means "any character", the * means "0 or more of the preceeding character", so .* means "0 or more of any character". This matches anything in the filename after Foo and before the next pattern.

Characters in braces - the [] - match any single character that is inside the braces, so [13579] matches any odd number.

If you took out the ^ and the .* you'd end up with a pattern that matched files with names that contained "Foo" immediately followed by a single odd number, like "BooFoo9". It wouldn't limit the match to files that started with "Foo" and it wouldn't match any file that had other characters between the "Foo" and the number, like "FooBar9".