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Permutations Possible for Six Digit Ordered Sample: 2,3,4,5,6,9











































Probability.

1. How many two digit numbers can be formed from the six digits: 2,3,4,5,6,9?

2. How many of these two digit numbers are less than 80?

3. How many of these numbers are even?

4. How many of these numbers are odd?

5. How many of these numbers are multiples of 5?

When completing the computations, repetitions are not permitted.


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Jun 30, 2012
Permutations Possible for Six Digit Ordered Sample
by: Staff

1. How many two digit numbers can be formed from the six digits?

Since this is a two digit number, write the number of choices available for the first number, and then write the number of choices available for the second number.

1st number: 6 choices available (you can choose any of the 6 numbers)

**Remember, repetition is not allowed.

2nd number: only 5 choices are available (you cannot choose the number which was used as the first number.

Number of two digit numbers possible = (# of choices for first number) * (#number of choices for second number)

Number of two digit numbers possible = 6 * 5

>>> Number of two digit numbers possible = 30 numbers



2. How many of these two digit numbers are less than 80?

The first number must be less than 8

There are 5 choices available for the first number.

There are also 5 choices available for the second number (not 6 choices, only 5 choices because repetition is not allowed.

Number of two digit numbers possible which are less than 80 = (# of choices for first number) * (#number of choices for second number)

Number of two digit numbers possible < 80 = 5 * 5

>>> Number of two digit numbers possible < 80 = 25 numbers



3. How many of these numbers are even?


To answer this question, start with the second number.

The second number must be an even number. There are only 3 choices: 2, 4, or 6.

Since repetition is not allowed, there are only 4 choices available for the first number.: 5 - 1 = 4


Number of two digit numbers possible which are less than 80 and even = (# of choices for first number) * (#number of choices for second number)


Number of two digit numbers possible < 80 and even = 4 * 3

>>> Number of two digit numbers possible < 80 and even = 12 numbers



4. How many of these numbers are odd?


To answer this question, start with the second number again.

The second number must be an odd number. There are only 3 choices: 3, 5, 9.

There are only 5 potential choices available for the first number.: 2,3,4,5,6. However, since repetition is not allowed:

If the second number is 9, the first number has 5 choices (2,3,4,5,6)

Number of two digit numbers possible < 80 and odd = 5 * 1 = 5


If the second number is 3 or 5, the first number has 4 choices.

Number of two digit numbers possible < 80 and odd = 4 * 2 = 8


>>> Total number of two digit numbers possible < 80 and odd = 5 + 8 = 13 numbers



5. How many of these numbers are multiples of 5?

Part 2. (above) shows that there are 25 two digit numbers possible which are less than 80.

To be a multiple of 5, the Second Number has only 1 possibility: the number 5

The first number can only be filled in 5 ways: 2, 3, 4, 6


Number of two digit numbers possible < 80 and multiples of 5 = 4 * 1


>>> Number of two digit numbers possible < 80 and multiples of 5 = 4



Thanks for writing.

Staff
www.solving-math-problems.com


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