How To Evaluate Binomial Coefficients | Summary and Q&A

TL;DR

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

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.

Transcript

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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.