Evaluate the binomial coefficient

Question

Evaluate the binomial coefficient: (14 11)  side note: 14 is on top of 11 in parentheses 

Answer 1

Hi Dalia!  

 

Another notation for this is 14C11 which may be read as, 14 choose 11.  It's a combination and order doesn't matter for combinations.  This notation can be found on a TI graphing calculator under the MATH, then PRB menu as nCr.  Here, n is 14 and r is 11.  Think about if we had 14 items or symbols.  How many ways could we take only 11 of them?

 

On the calculator,

 

type 14, then select nCr, then type 11, and hit ENTER.

 

By hand, you can use the formula, involving factorials, at the following link where k is being used for r.

http://mathworld.wolfram.com/BinomialCoefficient.html

If you're not sure what a factorial is, just ask.

 

I calculated 364 for the answer.  Please verify!

Answer 2

C(14,11) = 14!/(11!(14-11)!)

 

= 14*13*12*11!/(11!3!)

 

= 14*13*12/(3*2*1)

 

= 14*13*2

 

= (13+1)*13*2

 

= (169+13)*2

 

= (182)*2

 

= 364