Each student at State University has a student ID number con

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

Solution

Given, I.D. number consists of four digits followed by three letters.

In general, it would be of the form, __  __  __  __  __  __  __

Let us name the digits as D₁, D₂, D₃ and D₄ respectively.

And the letters as L₁, L₂ and L₃ respectively.

So we have the form, D₁  D₂  D₃  D₄  L₁  L₂  L₃

D₁ can be any one of 1, 2, 3, 4, 5, 6, 7, 8, 9 (since its given, first digit as non zero)

So, there are 9 ways to select the first digit.

D₂, D₃ and D₄ can be any one of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (Since its given, digits may be repeated)

So, there are 10 ways each to select the next three digits.

L₁ can be any one of A, B, C, D, E.

So, there are 5 ways to select the first letter.

And hence, there would be 4 ways to select the second letter L₂ (Since its given, letters may not be repeated)

Similarly, there would be 3 ways to select the third letter L3 (Since its given, letters may not be repeated)

So, the possible number of ways for, D₁  D₂  D₃  D₄  L₁  L₂  L₃  would be

9 x 10 x 10 x 10 x 5 x 4 x 3 = 540000

Hence, 540000 different student numbers are possible.