4.1 #3,8,11,12,16,18,44,51,55
4.3 #3,11,22,29,39

4.1 #8. No initials repeated: 26 * 25 * 24.

4.1 #12. 2^6 + 2^5 + 2^4 + ... + 2^0. (Don't leave out the empty string, it counts for one.)

4.1 #16. How many with x? 26^4 - 25^4.

4.1 #18.

  • floor(1000/7)
  • floor(1000/7) - floor(1000/77)
  • floor(1000/77)
  • floor(1000/7) + floor(1000/11) - floor(1000/77)
  • floor(1000/7) - floor(1000/77) + floor(1000/11) - floor(1000/77)
  • 1000 - (floor(1000/7) + floor(1000/11) - floor(1000/77))
  • 10*9*8
  • 5*9*8 (pick the 1s digit first, then the 10s, then the 100s)
  • 4.1 #44. 38 CS + 23 math - 7 joint = 54 in all

    4.3 #22a. Pick 5 people, and remove the selections of all men: (7+9 choose 5) minus (9 choose 5).

    b. Also remove the all women selections: (7+9 choose 5) minus (9 choose 5) minus (7 choose 5).