Question

2. A serial number for a TV begins with three letters, is followed by six numbers, and ends in one letter. How many different serial numbers are possible? Assume the letters and numbers

can be repeated.

Answer 1

1.1881376(10^{13}

Explanation:

Given that a serial number for a TV begins with three letters, is followed by six numbers, and ends in one letter.

Assume the letters and numbers can be repeated

Number of letters available are 26 and numbers available are 10 starting from 0 to 9.

First letter can be any of the 26 letters. Thus any letter selected has 26 choices and a number has 10 choices since repetition is allowed.

No of ways =
`26(26)(26)(10)^6 (26)`

=
`26^5 (10^6)\\=1.1881376(10^(13)`

Answer 2

4.5698 * 10^11 different serial numbers

Explanation:

For the first three letters, each letter has 26 different possibilities of being filled, and the letters can repeat, so the number of combinations for these three letters is:

26 * 26 * 26 = 17576

Then, we have six numbers, and each number has 10 possibilities that can be repeated, so the number of possibilities for these numbers are:

10 * 10 * 10 * 10 * 10 * 10 = 1000000 = 10^6

Now, for the last letter, we have 26 possibilities.

So, to find how many different serial numbers are possible, we just need to multiply the number of possibilities of each group:

17576 * 10^6 * 26 = 4.5698 * 10^11