I am really close to solving this but I am hung up!

Michael has a new cell phone and he’s having diﬃculty remembering the new ten-digit
phone number. His memory is bizarrely fragmented: he remembers that that the second,
fourth, and ﬁfth digits are either 7 or 9, the third and tenth digits are either a 2 or 4, there
are two zeros in the number, and the sum of the digits is 42. Given this information, how
many possibilities are there for Michael’s phone number?

Question

I am really close to solving this but I am hung up!

Michael has a new cell phone and he’s having diﬃculty remembering the new ten-digit
phone number. His memory is bizarrely fragmented: he remembers that that the second,
fourth, and ﬁfth digits are either 7 or 9, the third and tenth digits are either a 2 or 4, there
are two zeros in the number, and the sum of the digits is 42. Given this information, how
many possibilities are there for Michael’s phone number?

anonymous · Answer

I am supposed to include the inclusion-exclusion principal but I do not quite see how

anonymous · Answer

I'm not sure either...sorry!!  Interesting question though.

anonymous · Answer

Thanks for looking though!

anonymous · Answer

I'd say Michael should just call someone and check the caller ID... but that's just the logical response lol. Due to the fact that that it does not ask for his exact number and instead the possibilities, I suggest you simply write out the different numbers on a piece of blank printer paper as there aren't a terribly high amount.

skullpatrol · Answer

@ianguibas How can you say ab + ac is simpler than a(b +c)?

anonymous · Answer

@skullpatrol It honestly ISN'T but in mathematics it is considered to be the SIMPLIFIED form. That's a matter of theory though lol

skullpatrol · Answer

Thanks :-D