# Pascal’s triangle gives amethod for calculating the

## Problem 10E Chapter 1.2

Probability and Statistical Inference | 9th Edition

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Problem 10E

PROBLEM 10E

Pascal’s triangle gives amethod for calculating the binomial coefficients; it begins as follows:

The nth row of this triangle gives the coefficients for (a + b)n−1. To find an entry in the table other than a 1 on the boundary, add the two nearest numbers in the row directly above. The equation

called Pascal’s equation, explains why Pascal’s triangle works. Prove that this equation is correct.

Step-by-Step Solution:

Step 1 of 3:

We have to prove the pascal's equation

nCr = n-1Cr + n-1Cr-1

\And how the pascal's triangle works to find the binomial coefficients.

Step 2 of 3 :

We have to prove that

. nCr = n-1Cr + n-1Cr-1

Consider the RHS

n-1Cr + n-1Cr-1 =  +

=   [ (n-r)+r]

=    [n]

=

=    nCr

Hence the proof.

Step 3 of 3

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