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? {t-i, t-m, t-e, i-m, i-e, m-e} {t-i, t-m, t-e, i-t, i-m, i-e, e-t, e-m, e-i, m-i, m-t, m-e} {t-i, t-t, t-e, i-t, i-i, i-e, e-t, e-m, e-e, m-t, m-m, m-e} {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:

                        T-I    T-M     T-E

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

                      I-T     I-M     I-E

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

                     M-T     M-I    M-E

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

                         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}

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b