# Tricky inclusive numbersHomework

• tae3001
In summary, there are 90,000 5-digit numbers between 10,000 and 99,999 inclusive, 27,216 of which consist of 5 distinct digits. Out of these, 87,500 have at least one odd digit.

#### tae3001

A 5 digit number is one between 10,000 and 99,999 inclusive
1. How many 5 digits numbers are therE?
2. HOW MANY CONSISTOF 5 DISTINCT DIGITS?
3. hOW MANY 5 DIGIT NUMBERS CONTAIN AT LEAST ONE ODD DIGIT?

You don't need to shout.

So, what have you tried?

oops sorry..(LOL)
well first i did..
10,000-99,999 +1 =90000 thast question 1

I am stuck with question 2 and 3.. I want to divide by 5 or subtract.. but Iam warped//..

tae3001 said:
A 5 digit number is one between 10,000 and 99,999 inclusive
1. How many 5 digits numbers are therE?
2. HOW MANY CONSISTOF 5 DISTINCT DIGITS?
3. hOW MANY 5 DIGIT NUMBERS CONTAIN AT LEAST ONE ODD DIGIT?
(Note: In the following discussion, "Digit #1" is the LEFTMOST digit.)
SOLUTION HINTS:
2) → For 5 distinct digits, you have 9 choices for the 1st digit, 9 for the 2nd, 8 for the 3rd, 7 for the 4th, and 6 for the 5th. ⇒ ⇒ {Total Number}={? x ? x ? x ? x ?}.
3) → The numbers having at least 1 odd digit would be those left over after removing numbers having all even digits. In other words, {90,000 - (?)}. For the number having all 5 even digits, remember that digit #1 can be any of {2, 4, 6, or 8 ⇒ 4 choices}, and digits #2 thru #5 can be any of {0, 2, 4, 6, or 8 ⇒ 5 choices}.

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i am starting to see it.. but where would I select the distinct digits?? from 90,000 or would i choose
89999,89998,89997 and so on?
or would I take them from 10,000 and 99,999?

tae3001 said:
i am starting to see it.. but where would I select the distinct digits?? from 90,000 or would i choose
89999,89998,89997 and so on?
or would I take them from 10,000 and 99,999?
(In the following discussion, "Digit #1" is the Leftmost digit.)

Problem #2:
Digit #1 (Leftmost) is chosen from the set {1, 2, 3, 4, 5, 6, 7, 8, 9 ⇒ 9 choices}, and Digits #2 thru #5 are chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ⇒ 10 choices}, with the provision that each digit is distinct (different).
Thus, Digit #1 has 9 choices, Digit #2 has 9 choices {=(10 - 1) after eliminating #1's choice}, Digit #3 has 8 choices {=(10 - 2) after eliminating #1's & #2's choices}, Digit #4 has 7 choices {=(10 - 3) after eliminating #1's, #2's, & #3's choices}, and Digit #5 has 6 choices {=(10 - 4) after eliminating #1's, #2's, #3's, & #4's choices}.
{Total # of Numbers from 10000 to 99999 with All Distinct Digits} =
= (9)x(9)x(8)x(7)x(6) = (27216)

Problem #3:
The numbers having at least 1 odd digit would be those left over after removing numbers having all even digits. In other words, {90,000 - (# with All Even Digits)}. For the number having all 5 even digits, Digit #1 can be any of {2, 4, 6, or 8 ⇒ 4 choices}, and Digits #2 thru #5 can be any of {0, 2, 4, 6, or 8 ⇒ 5 choices}.
{Total # of Numbers from 10000 to 99999, inclusive, with At Least 1 Odd Digit} =
= 90000 - {(4)x(5)x(5)x(5)x(5)} = (87500)

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## 1. What are tricky inclusive numbers?

Tricky inclusive numbers are numbers that may be difficult to identify as either odd or even because they can fit into multiple patterns. For example, the number 6 can be evenly divided by 2 and 3, making it both an even and odd number.

## 2. How do you solve tricky inclusive numbers homework?

Solving tricky inclusive numbers homework involves identifying the patterns that the given numbers fit into and using mathematical principles to determine their correct classification. It may also involve using logic and critical thinking skills to find the most appropriate solution.

## 3. Can you give an example of a tricky inclusive number?

One example of a tricky inclusive number is 12. It can be divided evenly by 2, 3, 4, and 6, making it both an even and odd number. However, in this case, it is more commonly classified as an even number.

## 4. How can you check your answers when working with tricky inclusive numbers?

To check your answers, you can use a calculator or manually divide the number by different factors to see if it results in a whole number. You can also use patterns and logic to verify your solution.

## 5. Is there a trick to quickly identifying tricky inclusive numbers?

There is no specific trick to quickly identifying tricky inclusive numbers. It requires a thorough understanding of mathematical principles and good problem-solving skills. However, practicing with different examples can help improve your ability to identify these numbers more efficiently.