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?

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Answer 1 · 2016-01-31T08:29:10

#3,268,760# different ways to answer

Answer 15 only out of 25 questions then it is a combination problem.

Use #nCr=(n!)/((n-r)! r!)#

with #n=25# and #r=15#

#25C15=(25!)/((25-15)! 15!)#

#25C15=(25*24*23*22*21*20*19*18*17*16*cancel15!)/(10!cancel15!)#

#25C15=(25*24*23*22*21*20*19*18*17*16)/(10*9*8*7*6*5*4*3*2*1)#

#25C15=3268760# ways

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