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. $$^{15}C{11} \times 11! = ^{15}P_{11}$$