1. A toy shop sells 5 types of teddy bears and 3 types of toy cars. How many different teddy-and-car combinations can you choose?
   
   
2. A toy shop sells 5 types of teddy bears, 3 types of toy cars, and 4 types of spinning tops. How many different choices are there if you pick:
   a) one teddy bear, one toy car, and one spinning top?
   b) any two different toys?
   
   
3. How many four-digit numbers are there such that:
   a) only even digits are used?
   b) there is at least one even digit?
   (Hint: Even digits are 0, 2, 4, 6, 8.)
   
   
4. You flip a coin three times. How many different possible outcomes (sequences of heads and tails) are there?
   
   
5. Each square in a 2×2 grid is coloured either black or white. How many different ways are there to colour the grid?
   
   
6. In the fictional Mumbo-Yumbo language, the alphabet has just two letters: A and U. A “word” can be any sequence of up to 5 letters. How many different words are there in the Mumbo-Yumbo dictionary?
   
   
7. A football team has 11 players. In how many ways can you choose:
   a) a captain and a vice-captain (two different people)?
   b) two strikers (order doesn’t matter)?
   
   
8. How many ways can you place:
   a) a black rook and a white rook on a chessboard?
   b) a black king and a white king, such that they don’t attack each other?
   (Reminder: Rooks attack any square in the same row or column. Kings attack all adjacent squares.)
   
   
9. Charlie has 4 different-coloured counters. In how many different ways can he arrange them in a row?
   
   
10. How many five-digit numbers can be formed using only odd digits, such that each digit is different?
    (Hint: Odd digits are 1, 3, 5, 7, 9.)
    
    
11. Which are more numerous: seven-digit numbers that include the digit 1, or those that don’t contain the digit 1 at all?
    
    

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