How To Evaluate Binomial Coefficients

TL;DR

Learn how to evaluate the binomial coefficient using the formula and simplifying the expression.

Transcript

in this video we're going to talk about how to evaluate the binomial coefficient so let's go over the definition for it this expression which means n above r this is equal to n factorial over R factorial times n minus r factorial where N is a number equal to or greater than r n can't be less than R if R is 4 n could be 4 5 6 or some other non-negat... Read More

Key Insights

• #️⃣ The binomial coefficient is represented by n above r, where n is the total number of items and r is the number of items being chosen.
• 0️⃣ Zero factorial and one factorial are both defined as 1.
• 😀 When n is equal to r, or when r is 0, the binomial coefficient simplifies to 1.

Questions & Answers

Q: What is the formula for evaluating the binomial coefficient?

The formula for the binomial coefficient is n! / (r! * (n-r)!) where n is a number equal to or greater than r.

Q: How do you evaluate a factorial expression?

To evaluate a factorial expression, you multiply the number by all positive integers less than it, down to 1.

Q: What is the value of 8 above 3 in the binomial coefficient?

To evaluate 8 above 3, use the formula: 8! / (3! * 5!). Simplifying, we get 56 as the final answer.

Q: What is the value of 4 above 0 in the binomial coefficient?

To evaluate 4 above 0, use the formula: 4! / (0! * 4!). Since any number divided by itself is 1 and 0! is 1, the final answer is 1.

Q: What is the value of 7 above 5 in the binomial coefficient?

To evaluate 7 above 5, use the formula: 7! / (5! * 2!). Simplifying, we get 21 as the final answer.

Summary & Key Takeaways

• The binomial coefficient is defined as n above r and can be evaluated using the formula n! / (r! * (n-r)!).

• Factorial expressions can be evaluated by multiplying the number by all positive integers less than it, down to 1.

• When n is one unit higher than r, the binomial coefficient simplifies to n.