i ve found a couple of interesting problems for h/w , i have found solutions, although i am not entirely sure whether i am right or not.
1) In how many ways can we distribute 8 same balls into 3 Boxes:
- So that none of the boxes is empty?
- The 3rd box should have odd number of balls
- None of the boxes is empty AND the 3rd box must have odd number of balls.
I used the type of combinations with repetition. Due to many calcualtions i decided not to post my whole answer here , but if i am completely wrong ill post it here later.
2) There is a message that consists of 12 different symbols.This message is going to be sent through a transmition channel. The transmitter will additionally send 45 spaces between the symbols, with at least 3 spaces between each pair of symbols. In how many ways can the emitter send such a message?
My asnwer is: (again using combinations with repetition)