The serial number on a bill consists of a letter followed by seven digits and then a letter. How many different serial numbers are possible, given the letters and digits cannot be repeated?

Question

The serial number on a bill consists of a letter followed by seven digits and then a letter. How many different serial numbers are possible, given the letters and digits cannot be repeated?

Answer 1

For the first answer I get

26*25 permutations for letters and

10!/3! permutations for numbers

Multiply: 393,120,000

Answer 2

without repetition would exclude

plates such as C1234567C

or A1233567Z

26P(26-2) x 10P(10-7)

= 26P24 x 10P3

= 26!/24! x 10!/3!

=26x25 x 10x9x8x7x6x5x4

= 650 x 604,800

= 393,120,000

with repetition would

= (26^2)(10^7)

= 276 x 10^7

= 2.76 x 10^9

= 2.76 billion

= 2 billion 760 million

= 2,760,000,000

It's unclear why they would want to exclude repetition as it doesn't mean the license plates or serial numbers repeat, just that a digit repeats. C1234566B and C1234656B have a digit repeat, but the serial numbers are different.