High School Pre-Cal

Question

Which of the following is equivalent to the coefficient of the a^5b^4 term in the binomial expansion below?

(A+B)^9

 

A. ₉ C₃

 

B. ₉P₃

 

C. ₉P₄

 

D. ₉P₄

Answer 1

One of the answers C. or D. should be ₉C₄. That is the correct answer. 

 

The exponents are 4 and 5. So, the index after should match one of the two numbers. All coefficients of the binomial expansion are combinations, so that is why it should be 9-choose-4, which is the same as 9-choose-5.