Each Sunday the hymns to be sung are displayed on a hymn-board using numbered cards. The cards have the digits 0 to 9 on them. The hymn book has 750 hymns in it. Three different hymns are sung each service.
a) What is the smallest number of cards the church must have to be able to display any combination of 3 hymns?
b) If the number 6 can be used as an upside-down 9, how many cards can be saved from your answers to (a)?
I will need 2 zeros (0 can't be in front)
3 ones
3 twos
3 fours
...
3 sevens
2 eights
2 nines
total = 29
for b) we can save the 2 nines, (the 3 sixes will suffice)
so they can save 2 cards