Question

NO LINKS!!

Find the binomial coefficient

( 11)
(6)

Evaluate using Pascal's Triangle

4_C_1

Answer 1

• 462; 4

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The binomial coefficients can be found using Pascal's triangle.

Remember the rows are numbered starting from the second one on the top, and the first element is skipped in every row.

For the first one, follow the 11th row and 6th column, it is number 462, and for the second one follow the 4th row and 1st column, this is number 4, see the attached for both.

Calculation of the binomial coefficient is as follows:

• 
  `\[ \binom{11}{6} = _(11)C_6=\cfrac{11!}{6!(11-6)!}=\cfrac{6!*11*10*9*8*7}{6!5!} =\cfrac{11*10*9*8*7}{5*4*3*2} =462`

• 
  `\[ \binom{4}{1} = _4C_1=\cfrac{4!}{1!(4-1)!} =\cfrac{4!}{3!} =\cfrac{3!*4}{3!} =4`