Clayton places tiles that spell the word time in a bowl. He draws one tile from the bowl and then without replacing it, draws another tile: What is the sample space of the event representing the letters picked in the two draws?
A
{T-I, T-M, T-E, I-M, I-E, M-E}
B
{T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E}
C
{T-I, T-T, T-E, I-T, 1-1, 1-E, E-T, E-M, E-E, M-T, M-MM-E}
D
{T-I, T-M, T-E, T-T, I-T, I-M, I-E, I-I, E-T, E-M, E-I, E-E, M-T, M-T, M-E, M-M}

The sample space of events that represent the picking out of letters at two draw without replacing is:

     {T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E}

Step-by-step explanation:

Since, there are four choice of drawing a first tile:

             T     I     M     E

and now:

If first tile is drawn as T then the outcome corresponding to T on second draw are:

                        T-I    T-M     T-E

(T-T is not possible since there is no replacement of first tile )

Similarly if I is drawn on first draw then the outcome corresponding to I in second draw is:

                      I-T     I-M     I-E

(I-I is not possible since there is no replacement of first tile )

If M is drawn on first draw then the outcome corresponding to M in second draw is:

                     M-T     M-I    M-E

(M-M is not possible since there is no replacement of first tile )

Now if E is drawn on first draw then the outcome corresponding to E in second draw is:

                         E-T     E-I      E-M    

(E-E is not possible since there is no replacement of first tile )

Hence, total outcomes are:

      {T-I, T-M, T-E, I-T, I-M, I-E, E-T, E-M, E-I, M-I, M-T, M-E}