PASCAL’S TRIANGLE

DEPARTMENT OF ELECTRONICS ; COMMUNICATION

ENGINEERING

SYNOPSIS

Academic Year : 2018 – 2019

Year : IV

Sem : VII

Sec : A

Dept. of ECE, NHCE Page 1

PASCAL’S TRIANGLE

PASCAL’S TRIANGLE

Chapter 1

1.1 Introduction

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In mathematics, Pascal's triangle is a triangular array of

binomial coefficients.

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The rows of Pascal's triangle are numbered

starting with row 0 at the top (the zero-th row).

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The numbers in each row are numbered from the left beginning

With 0.

1.2 Pascal’s triangle(10 rows)

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PASCAL’S TRIANGLE

1.3 Interesting properties

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The diagonals going along the left and right edges contain

only 1's.

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The diagonal next to the first diagonal contains all the natural

numbers in order starting from 1.

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The next pair of diagonal contain the

triangular numbers in order i.e., 1,3,6 and so on.

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The next pair of diagonals contain the tetrahedral numbers in

Order.

1.4 Applications of Pascal’s Triangle

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Binomial expression

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Probability

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Combinations

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PASCAL’S TRIANGLE

Chapter 2

2.1 Fibonacci series

2.2 Binomial expression

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(a+b)^2 = 1a^2 + 2(ab)+ 1b^2

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The above representation is the coefficient of the expanded

Values that follows the Pascal’s triangle according to the power.

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PASCAL’S TRIANGLE

2.3 Probability

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Pascals Triangle can show you how many ways heads and

tails can combine. This can be used to find the probability of

any combination.

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In the following slide, H represents Heads and T represents

Tails

Probability; coin toss example

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For example, if a coin is tossed 4 times, the possible

combinations are:-

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HHHH

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HHHT, HHTH, HTHH, THHH

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HHTT, HTHT, HTTH, THHT, THTH, TTHH

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HTTT, THTT, TTHT, TTTH

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TTTT

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From the above we can say that the pattern is 1, 4, 6, 4 1

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The total number of possibilities can be found by adding all

the numbers together.

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Let us take an example of combinations.

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PASCAL’S TRIANGLE

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If there are 5 marbles of different colours,

How many different combinations can be made if two marbles

are taken out.

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10. This is taking note that the rows start with row 0 and the

position in each row also starts with 0.

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PASCAL’S TRIANGLE

Chapter 3

3.1Flowchart

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PASCAL’S TRIANGLE

3.2 Code

#include

long fun(int y)

{

int z;

long result = 1;

for( z = 1 ; z