Question

Each student at State college has a student I.d number consisting of eight digits ( the first digit is nonzero, and digits may be repeated) followed by two of the letters A,B,C,D,and E (letters may not be repeated). How many different student numbers are possible

Answer 1

Answer:

1,800,000,000 ways

Explanation:

Given

$Digits: 8$

$Alphabets: 2$

Required

Number of ways of selection

From the 8 digits; the first must be nonzero (i.e. any of 1 - 9).

There are 9 ways of selecting this:

The other 7 digits could be any of the 10 digits and there may be repetition.

Each of the digits can be selected in 10 ways. So, the number of ways of selecting the 7 digits is: $10^7$

For the alphabets:

The first can be selected from the $5$ letters while the second can be selected from the remaining $4.$

So, the number of ways the alphabets can be selected is: $5 * 4$

Total number of selection is:

$Selection = First\ Nonzero* The\ 7\ other\ digits\ * The\ alphabets$

$Selection = 9* 10^7 * 5 * 4$

$Selection = 1800000000$