DEPARTMENT OF ELECTRONICS ; COMMUNICATION
Academic Year : 2018 – 2019
Year : IV
Sem : VII
Sec : A
Dept. of ECE, NHCE Page 1
In mathematics, Pascal's triangle is a triangular array of
The rows of Pascal's triangle are numbered
starting with row 0 at the top (the zero-th row).
The numbers in each row are numbered from the left beginning
1.2 Pascal’s triangle(10 rows)
Dept. of ECE, NHCE Page 2
1.3 Interesting properties
The diagonals going along the left and right edges contain
The diagonal next to the first diagonal contains all the natural
numbers in order starting from 1.
The next pair of diagonal contain the
triangular numbers in order i.e., 1,3,6 and so on.
The next pair of diagonals contain the tetrahedral numbers in
1.4 Applications of Pascal’s Triangle
Dept. of ECE, NHCE Page 3
2.1 Fibonacci series
2.2 Binomial expression
(a+b)^2 = 1a^2 + 2(ab)+ 1b^2
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
Pascals Triangle can show you how many ways heads and
tails can combine. This can be used to find the probability of
In the following slide, H represents Heads and T represents
Probability; coin toss example
For example, if a coin is tossed 4 times, the possible
HHHT, HHTH, HTHH, THHH
HHTT, HTHT, HTTH, THHT, THTH, TTHH
HTTT, THTT, TTHT, TTTH
From the above we can say that the pattern is 1, 4, 6, 4 1
The total number of possibilities can be found by adding all
the numbers together.
Let us take an example of combinations.
Dept. of ECE, NHCE Page 5
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
Dept. of ECE, NHCE Page 7
long fun(int y)
long result = 1;
for( z = 1 ; z