Please help me to use the terms "various" and "a various" properly. Sometimes it is confusing. How about here? Can I use both of them here?

... can be performed using a various (various???) functions ...

Sorry, can you also tell me the difference in usage for the phrases "both of something" and "the both of something." Like the underlined part above, I sometimes am confused whether I should use "the both of them" or "both of them." Help.
using a various functions
No a.

Both of them
is fine
the other seems strange to me,
and Swan says that the should not be used before both
check both)
but look , I find enough usage with it at The New York Times (which is supposed to have educated writers/editors). Strange to me, again.

  • White Lies

    ... now estranged from the both of them and working as a nurse ...

    March 10, 2002 - By Tom Shone (NYT) - Arts - Review - 1849 words
  • Down the Years, a Call to Arms

    ... more action than the both of them together.'' That ...

    October 28, 2001 - By JIM O'GRADY (NYT) - New York and Region - News - 2756 words
  • Documents Allege Abuse of Nuns by Priests

    ... good' for the both of them,'' Father Vitillo ...

    March 21, 2001 - By CHRIS HEDGES (NYT) - World - News - 1068 words
  • PRO BASKETBALL; For 2 Pacers, 13 Years of Dues Pay Off With First Trip to Finals

    ... so long, the both of them,'' Perkins said ...

    June 3, 2000 - By LIZ ROBBINS (NYT) - Sports - News - 820 words
  • Elevating the Broadway Pit; A Legendary Conductor Shapes Musicals With His Baton

    ... creative years for the both of them,'' he said ...

    April 19, 2000 - By ROBIN POGREBIN (NYT) - Theater - News - 1642 words
  • Comments  

    Re: a various or various

    Hi Believer,

    In the first example, I would use various without the "a". The noun functions is in plural, and therefore does not require an article "a". You could say:

    ...can be performed using functions. The adjective "various" can the be inserted before the noun:

    ....can de perfomed using various functions.

    You could always rewrite the phrase so it says: ...can be performed using a variety of functions, if you care to emphasize the variety.

    Your second example does not require the article "the". The correct phrase is ....go ahead and take both of them. Maybe the similar expression...go ahead and take them both...is confusing you.

    I hope this helps,