SOLUTION: Call an integer dangerous if no two of its digits are equal and no digit is 2. Call an integer sexy if all its digits are odd. How many four-digit integers are either sexy or dange

Question 1065991: Call an integer dangerous if no two of its digits are equal and no digit is 2. Call an integer sexy if all its digits are odd. How many four-digit integers are either sexy or dangerous?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The 1st digit must exclude 0 or 2, so
there are 8 choices for the 1st digit
---------------------------------
The 2nd 2nd digit excludes the 1st digit
and 2, so there are 8 choices
---------------------------
The 3rd digit excludes 1st and 2nd digits
and 2, so there are 7 choices
--------------------------
There are 6 choices for the 4th digit
-----------------------------------
There are - dangerous numbers
--------------------------------------------
So there are no overlaps with sexy integers
count the number of dangerous integers
that have all odd digits
------------------------------------------
5 choices for the 1st ( dangerous integer ) digit
are odd
-------------------------------------------
4 choices for the 2nd digit are odd
---------------------------------
3 choices the the 3rd are odd
-----------------------------
2 choices for the 4th are odd
-----------------------------
There are dangerous numbers that are sexy
-----------------------------

There are 2568 dangerous numbers that are NOT sexy
---------------------------
There are sexy numbers
-------------------------------------------
There are 4 digit numbers
that are EITHER sexy or dangerous
--------------------------------------
Definitely get a 2nd opinion on this!!!
I could easily be missing something

RELATED QUESTIONS
If all three digits of a three-digit integer are the same, then if that integer is... (answered by AnlytcPhil)

Consider any positive three-digit integer that has all of its digits distinct and none... (answered by ankor@dixie-net.com)

a no. has two digits whose sum is 14. if 36 is added to the no., its digit are... (answered by ptaylor)

Please help me to solve this problem,,, In an integer between 10 and 100, the unit's... (answered by ikleyn)

Find a 3 digit no. such that its digits are in geometric progression and digits of number (answered by ikleyn)

Find all 2-digit positive integers in which the difference between the integer and the... (answered by greenestamps)

1.Find three consecutives odd integers such that the product of the first and third... (answered by ankor@dixie-net.com)

How many ways are there to write a three digit positive integer using the digits 1 3 7 &... (answered by solver91311)

This is a question my teacher assigned if we want to do, it is extra, but I would like to (answered by KMST)