How to calculate 200C65 (for binomial distribution formula)

In summary, the conversation discusses different methods of calculating 200C65, including using a brute force solution, Stirling's formula for approximating large factorials, and Mathman's approach using a computer or programmable calculator. It is noted that Stirling's formula may not provide an exact answer, but can be used to check the accuracy of other methods. The conversation ends with a suggestion to use the upper and lower bound formulae for a sanity check on the answer.
  • #1
socrates_1
26
0
Hi, I have tried to calculate 200C65 on my calculator but the calculator gives an error. Do u know how to do it?
I also tried to calculate it through the formula with the ! but doesn't give an answer.
 
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  • #2
socrates_1 said:
Hi, I have tried to calculate 200C65 on my calculator but the calculator gives an error. Do u know how to do it?
I also tried to calculate it through the formula with the ! but doesn't give an answer.

I don't know the limit on number size for your calculator, but the simplest brute force solution would be:
(200/65)(199/64)...(136/1)
 
  • #3
Stirling's formula is a way of approximating large factorials.

Mathman's approach is easy and exact if you have a computer or programmable calculator, but error prone if you are doing it manually. Stirling's approximation is (according to Wikipedia) accurate to about 1% for 65!. [strike]That's fine for your application, since you know that 200!/135!65! must be an integer - just use the approximation, do the division, and round off.[/strike]

Edit: Sorry - it's been a long day. 1% of 200! is a big number; my approach will not do if you need an exact answer. However, it'll tell you right off if your calculator can handle the answer. Also, you can use the upper and lower bound formulae to get a sanity check on your answer.

Off to bed now...
 
Last edited:

1. What is the binomial distribution formula?

The binomial distribution formula is a mathematical equation used to calculate the probability of a certain number of successes in a specific number of independent trials. It is often used in statistics and probability to analyze data and make predictions.

2. How is 200C65 calculated?

200C65 is calculated using the binomial distribution formula, specifically the combination formula. The formula is nCr = n!/(r!(n-r)!), where n is the total number of trials and r is the number of successful outcomes. In this case, n = 200 and r = 65, so the calculation would be 200!/(65!(200-65)!) = 200!/(65!135!).

3. What does the number 200C65 represent?

The number 200C65 represents the number of different ways that a specific outcome can occur in a set of 200 independent trials. In this case, it represents the number of ways that 65 successes can occur in 200 trials.

4. How is the binomial distribution formula used in real life?

The binomial distribution formula is used in various fields such as physics, biology, finance, and business to analyze data and make predictions. For example, it can be used to calculate the probability of a certain drug being effective in a clinical trial, or the likelihood of a certain stock price increasing over time.

5. What are the limitations of the binomial distribution formula?

One limitation of the binomial distribution formula is that it assumes all trials are independent and have the same probability of success. In real life, this may not always be the case. Additionally, the formula is most accurate when used with a large number of trials.

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