How to Use Pascal’s Triangle?
We use the Pascal triangle to find the various case of the possible outcomes in probability conditions. This can be understood by the following example, tossing a coin one time we get two outcomes i.e. H and T this is represented by the element in the first row of Pascal’s Triangle.
Similarly tossing a coin two times we get three outcomes i.e. {H, H}, {H, T}, {T, H}, and {T, T} this condition is represented by the element in the second row of Pascal’s Triangle.
Thus, we can easily tell the possible number of outcomes in tossing a coin experiment by simply observing the respective elements in the Pascal Triangle.
The table below tells us about the cases if a coin is tossed one time, two times, three times, and four times, and its accordance with Pascal’s Triangle
Number of Tosses |
Possible Outcomes |
Elements in Pascals Triangle |
---|---|---|
1 |
{H}, {T} |
1 1 |
2 |
{HH}, {HT}, {TH} , {TT} |
1 2 1 |
3 |
{HHH}, {HHT}, {HTH}, {THH} {HTT}, {THT}, {TTH}, {TTT} |
1 3 3 1 |
4 |
{HHHH}, {HHHT}, {HHTH}, {HTHH}, {THHH}, {HHTT}, {HTHT}, {HTTH}, {THHT}, {THTH}, {TTHH}, {HTTT}, {THTT}, {TTHT}, {TTTH}, {TTTT} |
1 4 6 4 1 |
Pascal’s Triangle
Pascal’s Triangle is a numerical pattern arranged in a triangular form. This triangle provides the coefficients for the expansion of any binomial expression, with numbers organized in a way that they form a triangular shape. i.e. the second row in Pascal’s triangle represents the coefficients in (x+y)2 and so on.
In Pascal’s triangle, each number is the sum of the above two numbers. Pascal’s triangle has various applications in probability theory, combinatorics, algebra, and various other branches of mathematics.
Let us learn more about Pascal’s triangle, Its construction, and various patterns in Pascal’s Triangle in detail in this article.
Table of Content
- What is Pascal’s Triangle?
- What is Pascal’s Triangle?
- Pascal’s Triangle Definition
- Pascal’s Triangle Construction
- Pascal’s Triangle Formula
- Pascal’s Triangle Binomial Expansion
- How to Use Pascal’s Triangle?
- Pascal’s Triangle Patterns
- Addition of Rows
- Prime Numbers in Pascal’s Triangle
- Diagonals in Pascal’s Triangle
- Fibonacci Sequence in Pascal’s Triangle
- Pascal’s Triangle Properties
- Pascal’s Triangle Examples