Solutions

  1. Answer: P (1000, 3)

  2. Answer: With repetition: 268 ≈ 2.0883 × 1011. Without repetition: P (26, 8) ≈ 6.2991 × 1010

  3. Answer: 15!

  4. Answer:
    1. P (15, 5) = 360360
    2. 2 · 14 · 13 · 12 · 11 = 48048

  5. Answer: 2 · P (3, 3) = 12

  6. Answer:
    1. P (4, 2) = 12
    2. P (n; 2) = n · (n − 1)
    3. Case 1: m > n. Since the coordinates must be different, this case is impossible.
      Case 2: m ⩽ n.P (n ; m).