Run wc and display only the word count

By default, wc print result along with filenames. If you want only the result, you must make wc read input from stdin:

</usr/share/dict/words wc -w > ~/dicwords.txt

With your current solution, you can use some other tools to get only the result from wc, like cut, awk, grep...

wc -c /usr/share/dict/words | cut -d' ' -f1 > ~/dicwords.txt