Solutions

  1. Answer: If there are m horses in race 1 and n horses in race 2 then there are m · n possible daily doubles.

  2. Answer: 72 = 4 · 6 · 3

  3. Answer: 720 = 6 · 5 · 4 · 3 · 2 · 1

  4. Answer: If we always include the blazer in the outfit we would have 6 outfits. If we consider the blazer optional then there would be 12 outfits. When we add a sweater we have the same type of choice. Considering the sweater optional produces 24 outfits.

  5. Answer:
    1. 28 = 256
    2. 24 = 16. Here we are concerned only with the first four bits, since the last four must be the same.
    3. 27 = 128, you have no choice in the last bit.

  6. Answer:
    1. 16
    2. 31

  7. Answer:
    1. 3
    2. 6

  8. Answer: 18

  9. Answer:
    2. 56

  10. Answer: 2n − 1 − 1 and 2n − 2