Question

How can you use the pattern in the table of combinations to find a number in pascals triangles​

Answer 1

The pattern in the table of combinations can be used to find a number in Pascal’s triangle because each number in the triangle is the sum of the two numbers above it. For example, the number six is in the center of row four: which is the sum of three and three in the row above it. The very first and very last number in any row are always going to be one.

Answer 2

Check the values in the combination with respect to the pascal's triangle. Use the value of n to determine the row, and the value of r to determine the exact number on the row.

Explanation:

For example, 5nCr2

Cr = combination

n= 5

n = 5th row

r= 2

r= the 2nd number on the fifth row after 1. When we count we don't include 1.

Using pascals triangle,

5nCr2 = 10

A sample of pascal's triangle has been attached to the solution.

Pascal's triangle involves the addition of numbers above to get the values below. The first number in the triangle is one. The next row, one is written twice forming a triangle. Let there be space between each number in the row.

1st row: 1

= 0 1 0

2nd row: 0+1 1+0 = 1 1

= 0 1 1 0

3rd row: 0+1 1+1 1+0 = 1 2 1

= 0 1 2 1 0

4th row: 0+1 1+2 2+1 1+0 = 1 3 3 1

The other rows follow same process.