Chapter 6 - Section 6.1 - The Basics of Counting - Exercises - Page 398: 54

8268650 different initials

Number of 2 different initials = 26$\times$25 = 650 Number of 3 different initials = 26$\times$25$\times$24 = 15600 Number of 4 different initials = 26$\times$25$\times$24$\times$23 = 358800 Number of 5 different initials = 26$\times$25$\times$24$\times$23$\times$22 = 7893600 Total number of initials = 7893600 +358800 +15600 + 650 = 8268650