Calculate
• 4C0, 4C1, 4C2, 4C3 and 4C4
• 4C0=1, 4C1=4, 4C2=6, 4C3=4 and 4C4=1
• Where have you seen this sequence of
numbers before?
Pascal’s Triangle Revisited
0C0
1C0
2C0
3C0
4C0
2C1
3C1
4C1
1C1
2C2
3C2
4C2
3C3
4C3
4C4
nth line nC0 nC1 nC2 etc…
(starts on the 0th line)
Implication: Pascal’s Formula
0C0
1C0
2C0
3C0
4C0
1C1
2C1
3C1
4C1
2C2
3C2
4C2
3C3
4C3
4C4
Notice that each entry is equal to the sum of 2
entries from a proceeding row.
For example: 4C2=3C1 + 3C2
This is known as Pascal’s Formula:
nCr=n-1Cr-1
+ n-1Cr
Binomial Theorem
Do you see a pattern in the coefficients?
Pascal’s Triangle
1
1
1
1
2
1
1
1
1
6
3
3
4
5
1
6
10
15
1
4
10
20
1
5
15
1
6
1
nth line nC0 nC1 nC2 etc…
(starts on the 0th line)
Example: Expand (x+y)6
• Try it yourself, use row 6 from Pascal’s
Triangle (the seventh row counting from
the top) or 6C0, 6C1 … 6C6 as the
coefficients.
Another Example
1 4
(2 x  )
y
HINT: expand (a+b)4 then
sub in 2x for a and 1/y for b.
Practice
• Page 293
• Questions 1 to 12