A test consists of 25 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?

Question

anonymous · Answer

guess what?  $_{25}C_{15}$

anonymous · Answer

25 C 10    =   (25)! / [(15)! x (10)!]

= (25)(24)(23)(22)(21)(20)(19)(18)(17)(16)

      divided by

   (10)(9)(8)(7)(6)(5)(4)(3)(2)(1)

A lot of scientific calculators have "combination" calculations in them.  If yours does not, then just do:

(25)! / [(15)! x (10)!]

And x! means (x)(x - 1)(x - 2) . . . (3)(2)(1)

anonymous · Answer

You should get:

3268760

as your answer if your calculations are done right.

anonymous · Answer

All good now, @melodylovesunicorns ?

anonymous · Answer

Thank you tcarroll010!

anonymous · Answer

uw!  Good luck to you in all of your studies and thx for the recognition! @melodylovesunicorns

anonymous · Answer

btw,  25 C 15   and 25 C 10 are equivalent.  Interesting!

anonymous · Answer

Because both have :

(15!)(10!) 

in the denominator!

anonymous · Answer

thx for the recognition! @satellite73