SOLUTION: one professor grades homework by randomly choosing 5 out of 15 homework problems to grade. How many different groups of 5 problems can be choosen from the 15 problems?

Question 249375: one professor grades homework by randomly choosing 5 out of 15 homework problems to grade. How many different groups of 5 problems can be choosen from the 15 problems?
Found 2 solutions by dabanfield, checkley77:
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
one professor grades homework by randomly choosing 5 out of 15 homework problems to grade. How many different groups of 5 problems can be choosen from the 15 problems?
The formula for combinations of k things taken from n things is:
C(n,k) = n!/((k!*(n-k)!)
In this case n = 15 and k = 5 so we have:
C(15,5) = 15!/(5!*10!)
You will need to multiply out the factorials and finish the calculation for the final answer.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
(15)
(5 )
THIS IS A COMBINATION PROBLEM.
15 ITEMS TAKEN 5 AT A TIME OR:
15!/[5!(15-5)!]
15*14*13*12*11*10*9*8*7*6*5*4*3*2*1/[(5*4*3*2*1)(10*9*8*7*6*5*4*3*2*1]
NOW CANCEL OUT TO GROUP (10*9*---*2*1)
15*14*13*12*11/5*4*3*2*1
360,360/120=3,003 GROUPS OF 5 PROBLEMS CAN BE CHOSEN.
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