How many possibilities are there for the 3?

  • Thread starter Jennifer1990
  • Start date
In summary, the conversation discusses finding the probability of arranging six chosen digits without replacement in a way that places the digits 2 and 3 in the correct order but not consecutively. There is some confusion about the numerator, with one person thinking it is 5C4 * 1 * 1 and another person thinking it is 5/14. Further discussion and clarification is needed from Jennifer to determine the correct answer.
  • #1
Jennifer1990
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Homework Statement


Six digits from the numbers 2, 3, 4, 5, 6, 7, 8 are chosen and arranged in a row without replacement. Find the probability that the digits 2 and 3 appear in the proper order but not consecutively


Homework Equations





The Attempt at a Solution


i know that the denominator is 7!, however I'm having trouble finding the numerator. I think that the numerator is 5C4 * 1 *1 however the answer is 5/21
 
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  • #2


Suppose that 2 is in the 1st place. How many possibilities are there for the 3?
If 2 is in the 2nd place, in how many places can you put 3?
And if 2 is in the 3rd position?
etc.
 
  • #3


i believe the answer is actually 5/14
 
  • #4


I got something else than 5/21 as well (5/14 sounds familiar). But we will know as soon as Jennifer posts again.

Perhaps she has misquoted the answer, or didn't state the complete question.
 

FAQ: How many possibilities are there for the 3?

What is the total number of possibilities for the 3?

The total number of possibilities for the 3 is 3. This is because the number 3 only has three possible combinations: 3, 2+1, and 1+2.

What is the probability of getting 3 when rolling a three-sided die?

The probability of getting 3 when rolling a three-sided die is 1/3 or approximately 33.33%. This is because there is only one side with the number 3 out of three total sides.

How many different ways can the number 3 be expressed as the sum of two positive integers?

The number 3 can be expressed as the sum of two positive integers in two ways: 3 = 1+2 and 3 = 2+1. This is because the order of the numbers in the sum does not matter.

What is the significance of the number 3 in mathematics?

The number 3 has many significant meanings in mathematics. It is the first odd prime number, the first number that is neither prime nor composite, and the first number that is the sum of two prime numbers (2+1). It also has religious and cultural significance in many civilizations.

How many factors does the number 3 have?

The number 3 has two factors: 1 and 3. This is because a factor is any number that can be multiplied by another number to get the original number, and 3 can only be multiplied by 1 and 3 to get itself.

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