SOLUTION: Prove that nCr is less than or equal to n+1Cr+1 . Hint: Make use of the fact that if A ≤ B then A/B ≤1.

Algebra ->  Probability-and-statistics -> SOLUTION: Prove that nCr is less than or equal to n+1Cr+1 . Hint: Make use of the fact that if A ≤ B then A/B ≤1.      Log On


   

Question 565266: Prove that nCr is less than or equal to n+1Cr+1
. Hint: Make use of the fact that if A ≤ B then A/B ≤1.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Pascal's triangle easily proves it, as



Since nC(r+1) is nonnegative, nCr <= (n+1)C(r+1).

Or, we can show that





Multiply both numerator and denominator by 1/(denominator)



Divide both sides by n!r!



This is true because we're choosing r objects out of n, so it is reasonable to assume r <= n.