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A social impact strategist is organizing a technology education initiative where participants can choose from 4 coding workshops, 6 design workshops, and 5 entrepreneurship workshops. If a participant randomly selects 3 workshops, what is the probability that they choose one from each category?
To find the probability of selecting one workshop from each category, we calculate the number of favorable outcomes and divide by the total number of outcomes.
First, calculate the total number of ways to choose 3 workshops from 15:
Next, calculate the number of ways to select 1 coding workshop from 4:
\[ \binom{4}{1} = 4 \]
Calculate the number of ways to select 1 design workshop from 6:
Calculate the number of ways to select 1 entrepreneurship workshop from 5:
\[ \binom{5}{1} = 5 \]
\[ 4 \times 6 \times 5 = 120 \]