Chapter 9.5, Problem 97E

To determine

To complete: the given table and determine the characteristic of Pascal’s Triangle illustrated by this table.

n	r	$C{}_r$	$C{}_{n-r}$
9	5
7	1
12	4
6	0
10	7

Answer to Problem 97E

n	r	$C{}_r$	$C{}_{n-r}$
9	5	126	126
7	1	7	7
12	4	495	495
6	0	1	1
10	7	120	120

This table illustrates the symmetry of Pascal’s Triangle.

Explanation of Solution

Concept Used:

Pascal’s triangle:

The n^th row of Pascal’s triangle gives the coefficients of ${\left(x+y\right)}^n$ .

In the Pascal’s triangle $C{}_r$ represents the r^th element of the n^th row of the Pascal’s triangle for $r=0,1,2,\mathrm{...},n$ .

Use this property to complete the table below:

n	r	$C{}_r$	$C{}_{n-r}$
9	5	126	126
7	1	7	7
12	4	495	495
6	0	1	1
10	7	120	120

This table illustrates the symmetry of Pascal’s Triangle.