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}

Question

Kai Ingram

Mathematics

9 February, 20:21

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}

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Answers (1)

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Uriel Beck · Answer 1

The problem can be represented in tree diagram as shown below. The combinations of drawing the first and the second tile is

TI IT MT ET

TM IM MI EI

TE IE ME EM

There are few combinations that actually give the same result in any order, for example, TI and IT are the same combinations. We can narrow down the combination to:

TI

TM

TE

MI

IE

ME

ET