A bag contains 10 identical pens, of which 4 are red and 6 are blue. 3 pens are taken out at random one…
A bag contains 10 identical pens, of which 4 are red and 6 are blue. 3 pens are taken out at random one after another. Find probability that all 3 are blue
$\frac{6}{10}$
$\frac{3}{10}$
$\frac{1}{6}$
$\frac{3}{6}$
Solution
Total number of balls $=10$
Number of Red balls $=4$
Number of Blue balls $=6$
Total Number of ways of choosing 3 balls $={ }^{10} C_3$
Number of ways of choosing 3 blue balls $={ }^6 C_3$
$\therefore$ Required Probability $=\frac{{ }^6 C_3}{{ }^{10} C_3}=\frac{1}{6}$
Hence, option (3) is correct.