What is the total combination for choosing 8 questions out of 10?

  • Thread starter caesarkim
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In summary, there are 45 total combinations if you have 10 questions and can only choose exactly 8 of them. This is determined by using the combination formula, where n is the number of choices and r is the number of items chosen. In this case, n=10 and r=8, giving a total of 45 combinations.
  • #1
caesarkim
there are 10 questions. i can choose only exact 8 questions.

what is the total combination?
 
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  • #2
45

10!/[(8!)(2!)]

Essentially, you have 10 choices for the first question you leave out, and 9 choices for the second question. This leads to 90 (10x9) combinations. But since it doesn't matter in which order you choose them, you've double counted (ie, you counted #1,#2 ans #2,#1 as different combinations), so divide by 2.

Njorl
 
  • #3
Njorl's given you the correct answer, but to expand this is a simple cominatrics question, your calculator will probably have a function that allows you to work it out, combinations are given by:

[tex]_nC_r \equiv \left(\begin{array}{c}n\\r\end{array}\right) \equiv \frac{n!}{r!(n-r)!}[/tex]

that is n different things taken r at a time, so in this case n = 10 and r = 8.
 
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1. What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. How is probability calculated?

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical definition of probability.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual results from conducting an experiment or collecting data.

4. Can probability be greater than 1 or less than 0?

No, probability cannot be greater than 1 or less than 0. A probability of 1 means that the event is certain to occur, while a probability of 0 means that the event is impossible.

5. How is probability used in real life?

Probability is used in various fields such as finance, weather forecasting, sports, and gambling. It helps in making informed decisions and predicting the likelihood of certain outcomes.

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