A bag contains 10 similar balls, of which 4 are blue and 6 are red. Three balls are taken at random from the bag one after the other without replacement. The probability that all the three balls drawn are red is:
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For problems involving drawing balls without replacement, calculate the probability using combinations for favorable and total outcomes.
Step 1: Calculate the total number of ways to choose 3 balls.
The total number of ways to choose 3 balls from 10 is given by:
\[
\binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120
\]
Step 2: Calculate the number of ways to choose 3 red balls.
The number of ways to choose 3 red balls from 6 is given by:
\[
\binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20
\]
Step 3: Compute the probability.
Thus, the probability that all 3 balls drawn are red is:
\[
\frac{\binom{6}{3}}{\binom{10}{3}} = \frac{20}{120} = \frac{1}{6}
\]
