Clayton places tiles that spell the word time in a bowl. He draws one tile from the bowl and then without replacing it, draws an

Question

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Clayton places tiles that spell the word time in a bowl. He draws one tile from the bowl and then without replacing it, draws an

other 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}

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-03-27T04:21:50+03:00

The scenario can be illustrated using a tree diagram as depicted below. The pairings of drawing the first and second tile form

TI IT MT ET
TM IM MI EI
TE IE ME EM

Certain combinations yield identical outcomes regardless of the order, such as TI and IT being equivalent. We can streamline the combinations to:

TI
TM
TE
MI
IE
ME
ET

AnnZ [12.3K] · Answer 2 · 2026-03-27T04:21:56+03:00

Answer:

The sample space for the selection of letters during two draws without replacement 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}

Explanation in steps:

There are four options for drawing a tile first:

T I M E

Then:

If the first tile is T, the possible outcomes for the second draw are:

T-I T-M T-E

(T-T is not an option as there is no replacement)

Similarly, if I is drawn first, the outcomes for the second draw would be:

I-T I-M I-E

(I-I cannot happen due to no replacement)

When M is picked first, the possible outcomes corresponding to M are:

M-T M-I M-E

(M-M isn’t viable since there's no replacement)

If E is the first draw, the outcomes for E in the second draw would be:

E-T E-I E-M

(E-E cannot occur due to no replacement)

Thus, the complete set of outcomes 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}