PASCAL’S TRIANGLE DEPARTMENT OF ELECTRONICS

PASCAL’S TRIANGLE

DEPARTMENT OF ELECTRONICS ; COMMUNICATION
ENGINEERING

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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)

Dept. of ECE, NHCE Page 2

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
Dept. of ECE, NHCE Page 3

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.

Dept. of ECE, NHCE Page 4

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.

Dept. of ECE, NHCE Page 5

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.
? The answer can be found in the 2nd place of row 5, which is
10. This is taking note that the rows start with row 0 and the
position in each row also starts with 0.
Dept. of ECE, NHCE Page 6

PASCAL’S TRIANGLE
Chapter 3
3.1Flowchart

Dept. of ECE, NHCE Page 7

PASCAL’S TRIANGLE
3.2 Code
#include
long fun(int y)
{
int z;
long result = 1;

for( z = 1 ; z

x

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