1. Objectives Find entries in Pascal’s triangle.
Use Pascal’s triangle to find combinations and probabilities.

2. 11.7 Pascal’s Triangle
Glossary Term
Pascal’s triangle

3. Rules and Properties Patterns in Pascal’s Triangle
Row n contains n + 1 entries.
The kth entry in row n is nCk – 1.
The sum of entries in row n is 2n.
nCk – 1 + nCk = n + 1Ck , where 0 < k  n

4. Rules and Properties Pascal’s Triangle and Two-Outcome Experiments
Perform n independent trials.
There are 2 equally likely outcomes.
Probability of event A occurring exactly k times:
P(A) =
nCk 2n

5. Key Skills Find entries in Pascal’s triangle.
Find the fourth entry in row 9.
n = 9; k = 4; k – 1 = 3 9!
6!3!
nCk – 1 = 9C3 =
= 84

6. Key Skills Use Pascal’s triangle to find probabilities.
You guess all the answers to 10 questions on a true-false test.
Find the probability of getting exactly 6 or exactly 7 correct answers.
number of possible outcomes: 210

7. Key Skills Use Pascal’s triangle to find probabilities. 10 questions
probability of exactly 6 or exactly 7 correct?
number of possible outcomes: 210
10C6
210
210
1024 =
P(exactly 6 correct) =
 0.21
10C7
210
120
1024 =
P(exactly 7 correct) =
 0.12

8. Key Skills Use Pascal’s triangle to find probabilities. 10 questions
probability of exactly 6 or exactly 7 correct?
number of possible outcomes: 210
P(exactly 6 correct)
 0.21
P(exactly 7 correct)
 0.12
P(exactly 6 or 7 correct)  = 0.33
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