Binomials raised to a power!

The Binomial TheoremPascal Triangle

Combination There are 5 top students in this class. If I would like to select 2 students out of these five to represent this class. How many ways are there for my choice?

List of the combinations ( order is not considered) :

(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5)

A symbol is introduced to represent this selection.

nCr or nCr or Cnr

nCr =

5C2 =

5C2 =

5C2 =

Combination

Your Turn

7C3

12C7

9C5

6C1

14C9

35

792

126

6

2002

Pascal Triangle

The binomial theorem is used to raise a binomial (a + b) to relatively large powers. To better

understand the theorem consider the following powers of (a+b):

Using these patterns the expansion

of looks like

and the problem now comes downto finding the value of each coefficient.

...

• Coefficients are arranged in a Pascal triangle.

• Summation of the indices of each term is equal to the power

(order) of the expansion.

• The first term of the expansion is arranged in descending

order after the expansion.

• The second term of the expansion is arranged in ascending

order order after the expansion.

• Number of terms in the expansion is equal to the power of

the expansion plus one.

The Binomial Theorem (Binomial expansion)