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mr_coffee

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I'm having troubles with the "multiplication rule" which states:

If an operation consist of k steps and

the first step can be performed in n_1 ways,

the second step can be performed in n_2 ways [regardless of how the first step was peformed],

.

.

.

the kth step can be performed in n_k ways [regardless of how the preceding seps were performed],

then the entire operation can be performed in (n_1)(n_2)...(n_k) ways.

The book does an example with a simliar problem, but small numbers, the book did the following:

10 to 99

They found out the following:

How many integers from 10 to 99?

answer: (number of ways to pick the first digit)(number of ways to pick the 2nd digit) = (9)(10) = 90.

How many odd integers from 10 to 99?

Well odd integers are: 1,3,5,7,9...a total of 5.

answer: (number of ways to pick the first digit)(number of ways to pick the 2nd digit) = (9)(5) = 45.

Number of integers with distinct digits:

answer: (number of ways to pick the first digit)(number of ways to pick the 2nd digit) = (9)(9) = 81.

**Number of odd integers with distinct digits:**

answer: (number of ways to pick the 2nd digit)((number of ways to pick the first digit)= (5)(8) = 40.

answer: (number of ways to pick the 2nd digit)((number of ways to pick the first digit)

First digit can't be 0, nor can it equal the 2nd digit.

**Thanks!**

Okay so I'm trying to apply that method to the bigger problem...

1000 to 9999

So for the number of odd integers with distinct digits...could i do the following:

(# of ways to pick 4th digit)(# of ways to pick 3rd digit)(# of ways to pick 2nd digit)(# of ways to pick 1st digit) = (5)(8)(7)(6) = 1680 ?

Okay so I'm trying to apply that method to the bigger problem...

1000 to 9999

So for the number of odd integers with distinct digits...could i do the following:

(# of ways to pick 4th digit)(# of ways to pick 3rd digit)(# of ways to pick 2nd digit)(# of ways to pick 1st digit) = (5)(8)(7)(6) = 1680 ?