Why do we use pascal triangle

Example 1: A coin is tossed three times, find the probability of getting exactly 2 tails. Answer: The probability of getting exactly two tails is Elements in the 6th row of the Pascals triangle are 1, 6, 15, 20, 15, 6, 1. Example 3: Find the sum of the elements in the 20th row of the Pascals triangle.

Using the Pascals triangle formula for the sum of the elements in the nth row of the Pascals triangle:. Answer: The sum of the elements in the 20th row is Pascals triangle can be used for various purposes in mathematics.

It is used in the binomial expansion of a polynomial, in probability , to find the number of combinations, and can be used to find the Fibonacci series. Pascals triangle is a very useful tool and has various properties that can be useful in various aspects of mathematics. Rules that Pascals triangle has is that we start with 1 at the top, then 1s at both sides of the triangle until the end.

The middle numbers, each is the sum of the two consecutive numbers just above it. Hence to construct a Pascals triangle we just need to add the two numbers just above the number. Hence if we want to find the coefficients in the binomial expansion, we use Pascals triangle. Pascal's formula is used to find the element in the Pascal triangle.

T here are 6 elements in the 5th row of the pascal triangle. The 5th row in Pascal's triangle is 1 5 10 10 5 1. Learn Practice Download.

Pascals Triangle Pascals triangle or Pascal's triangle is an arrangement of binomial coefficients in triangular form. Introduction to Pascals Triangle 2.

Question 2. In Pascals Triangle, each entry is the sum of the two entries above it. In which row of the triangle do three consecutive entries occur that are in the ratio ? Solution: Call the row x, and the number from the leftmost side t.

You must be logged in to post a comment. About The Author. Leave a Comment Cancel Reply You must be logged in to post a comment. Answer: go down to the start of row 16 the top row is 0 , and then along 3 places the first place is 0 and the value there is your answer, In fact there is a formula from Combinations for working out the value at any place in Pascal's triangle:. Notation: "n choose k" can also be written C n,k , n C k or n C k. The "! So Pascal's Triangle could also be an "n choose k" triangle like this one.

Note that the top row is row zero and also the leftmost column is zero. This can be very useful Pascal's Triangle also shows us the coefficients in binomial expansion :. View Full Image. It is called The Quincunx. Balls are dropped onto the first peg and then bounce down to the bottom of the triangle where they collect in little bins.