SME
Grade 11 Math · Problem type
Pascal’s rule: add the two above
Use this for “Find C(6, 2) from row 5 of Pascal’s triangle.”
Diagram
Row 6: 1, 6, 15, 20, 15, 6, 1; they add to 2⁶ = 64.
Entry 2 of row 6: C(6, 2) = 15.
The two above add to it: C(5, 1) + C(5, 2) = 5 + 10 = 15.
This is an example. Type your own values to start a new problem.
C(
n
,
k
)
=
L
+
R
=
E
Formulas
L
=
C(
n
−
1,
k
−
1)
5 = C(6 − 1, 2 − 1)
R
=
C(
n
−
1,
k
)
10 = C(6 − 1, 2)
E
=
L
+
R
15 = 5 + 10
Assumptions
•
Each row starts and ends with 1.
•
Each inside entry is the sum of the two entries above it: C(n, k) = C(n − 1, k − 1) + C(n − 1, k).
Step-by-step
WE KNOW
n = 6, k = 2
FIND
entry above left, C(n − 1, k − 1) (L), entry above right, C(n − 1, k) (R), entry C(n, k) (E)
Step 1 · Find entry above left, C(n − 1, k − 1): L
Use L = C(n − 1, k − 1)
The
entry
up
and
to
the
left,
in
row
n
−
1.
L
=
C(6
−
1,
2
−
1)
L
=
C(5,
1)
L
=
5
Step 2 · Find entry above right, C(n − 1, k): R
Use R = C(n − 1, k)
The
entry
up
and
to
the
right,
in
row
n
−
1.
R
=
C(6
−
1,
2)
R
=
C(5,
2)
R
=
10
Step 3 · Find entry C(n, k): E
Use E = L + R
Add the two entries above it.
E
=
5
+
10
E
=
15
Check
Put the numbers back in. Both sides should match.
5 = C(6 − 1, 2 − 1) ✓
10 = C(6 − 1, 2) ✓
15 = 5 + 10 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.