B.4 Theoretical Problems

  1. Prove \(^{n+1}C_r = ^nC_r + ^nC_{r-1}\)
  2. \(^nP_3 + ^nC_3 = 70; n=?\)
  3. Prove \(^nC_r = ^nC_{n-r}\)
  4. Arrange 11 players from 15 players.
    1. n = 5
    1. \(^{15}C{11} \times 11! = ^{15}P_{11}\)