Expert: Soroban - 7/17/2007

Question
Hello!
I was wondering if calculating the number of different ways 24 numbers can be picked out of 75 is the same as calculating how many distinctive Bingo cards can exist. (1 Bingo card has 24 numbers on it)? I suck at this type of calculations, factorial numbers make my head spin... thanks!

Answer
Hello, Anna!

What an interesting question!
   No, they are not the same.


If we randomly pick 24 number out of 1-to-75,
   the number of ways is:  C(75,24)

But we could get, for example, 1-to-24.
   And these would NOT be on a Bingo card.


Remember the structure of Bingo?

  "Under B", there are five numbers from the set 1-to-15.
  "Under I", there are five numbers from the set 15-to-30.
  "Under N", there are FOUR numbers from the set 31-to-45.
  "Under G", there are five numbers from the set 46-to-60.
  "Under O", there are give numbers from the set 61-to-75.


There are:  C(15,5) × C(15,5) × C(15,4) × C(15,5) × C(15,5) ways.

This is a HUGE number . . .
   My calculator says it's about:  111,007,923,800,000,000
.