Question

Analyze Pascal’s triangle to see if you can draw a link between the triangle and combinations.

Answer 1

Pascal’s triangle represents the values of combinations according to its rows.

Explanation:

In Pascal's triangle represents the coefficients of binomial.

It's top element is 1. This row is known as row 0.

All elements on the left and right sides are 1.

Each number is the numbers directly above it added together.

Formula of combination:

`^nC_r=(n!)/(r!(n-r)!)`

Using the above formula, the relation between Pascal's triangle and combinations is shown below:

Row 0:

`^0C_0=1`

Row 1:

`^1C_0=1,^1C_1=1`

Row 2:

`^2C_0=1,^2C_1=2,^2C_2=1`

Row 3:

`^3C_0=1,^3C_1=3,^3C_2=3,^3C_3=1`

Row 4:

`^4C_0=1,^4C_1=4,^4C_2=6,^4C_3=4,^4C_4=1`

Row 5:

`^5C_0=1,^5C_1=5,^5C_2=10,^5C_3=10,^5C_4=5,^5C_5=1`.

Therefore, the Pascal’s triangle represents the values of combinations according to its rows.