Different numbers from 1 to 10

Choosing random values and then throwing away those that you've already used is a bad idea. It makes the run-times longer as the pool of available numbers gets less since you're throwing away more and more.

What you want is a shuffle list which I would implement with the following code (pseudo-code since it's homework):

dim n[10]                 // gives n[0] through n[9]
for each i in 0..9:
    n[i] = i              // initialize them to their indexes
nsize = 10                // starting pool size
do 10 times:
    i = rnd(nsize)        // give a number between 0 and nsize-1
    print n[i]
    nsize = nsize - 1     // these two lines effectively remove the used number
    n[i] = n[nsize]

By simply selecting a random number from the pool then replacing it with the top number from that pool and reducing the size of the pool, you get a shuffle without having to worry about a large number of swaps up front. This is important if the number is high in that it doesn't introduce an unnecessary startup delay.

For example, examine the following bench-check:

<--------- n[x] ---------->
for x = 0 1 2 3 4 5 6 7 8 9  nsize  rnd(nsize)  output
---------------------------  -----  ----------  ------
        0 1 2 3 4 5 6 7 8 9     10           4       4
        0 1 2 3 9 5 6 7 8        9           7       7
        0 1 2 3 9 5 6 8          8           2       2
        0 1 8 3 9 5 6            7           6       6
        0 1 8 3 9 5              6           0       0
        5 1 8 3 9                5           2       8
        5 1 9 3                  4           1       1
        5 3 9                    3           0       5
        9 3                      2           1       3
        9                        1           0       9

You can see the pool reducing as you go and, because you're always replacing the used one with an unused one, you'll never have a repeat.

And now your homework consists of turning that into VB :-)

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And, since this homework is now almost certainly overdue (about a year ago), I'll post a VBA solution showing how to do it, for completeness.

Option Explicit
Option Base 0
Sub Macro1()
    Randomize
    Dim list(10) As Integer
    Dim i As Integer
    Dim size As Integer
    Dim pos As Integer
    Dim result As String

    For i = 0 To 9
        list(i) = i
    Next

    size = 10
    result = ":"
    For i = 1 To 10
        pos = Int(Rnd() * size)
        result = result & list(pos) & ":"
        size = size - 1
        list(pos) = list(size)
    Next

    MsgBox result
End Sub

This generated, on three separate runs:

:5:7:4:2:9:1:0:8:3:6:
:3:9:6:0:7:8:5:4:2:1:
:7:6:3:5:1:8:9:0:4:2: