Understanding Binomial Coefficients

This video tutorial explains how to evaluate binomial coefficients using factorials. It covers the definition, provides examples such as 8 above 3, 4 above 0, and 7 above 5, and discusses special cases where n equals r or r is 0. The video also explores scenarios where n is one unit above r, demonstrating the simplification process and the resulting values.

What is the formula for calculating a binomial coefficient?

• n! * r! / (n-r)!

• n! / (r! * (n-r)!)

• (n-r)! / (n! * r!)

• n! / (n-r)! * r!

In the expression 8 above 3, what is the value of 3 factorial?

• 3

• 6

• 9

• 12

What is the value of 4 factorial?

• 12

• 24

• 4

• 6

What is the value of any binomial coefficient when r is 0?

• 0

• n

• 1

• n!

What is the value of 0 factorial?

• n

• Undefined

• 1

• 0

What is the result of the binomial coefficient 7 above 5?

• 14

• 35

• 21

• 42

What is the value of a binomial coefficient when n equals r?

• n

• 1

• 0

• n!

If n is one unit above r, what is the value of the binomial coefficient?

• n-r

• n!

• r

• n

What happens to the binomial coefficient when n is one unit above r?

• It equals 0

• It equals n

• It equals n!

• It equals r

In the expression 9 above 8, what is the value of the binomial coefficient?

• 8

• 9

• 1

• 0