Question

A letter in the word TRANSFORMATION is chosenat random, then a coin is tossed three times. Howmany outcomes are possible?the

Answer 1

`72`

Step-by-step explanation

We want to find the number of possible outcomes.

To do this, we have to find the product of the number of outcomes from choosing a letter from the word and the possible outcomes from three coin tosses.

There are 9 distinct letters in the word TRANSFORMATION. They are:

T, R, A, N, S, F, O, M, I

Therefore, the number of possible outcomes is 9.

When a coin is tossed once, the number of possible outcomes is 2 (head or tail). When it is tossed 3 times, the number of possible outcomes is:

`\begin{gathered} 2\cdot2\cdot2=2^3 \\ \Rightarrow8 \end{gathered}`

Therefore, the number of possible outcomes for choosing the word and tossing a coin three times is:

`\begin{gathered} 9\cdot8 \\ \Rightarrow72 \end{gathered}`