A bag contains 6 blue, 8 yellow and 5 pink ball. If 3 ball are drawn at random. What is the probability that at least two are blue?
$\frac{215}{969}$
$\frac{235}{969}$
$\frac{215}{964}$
$\frac{215}{939}$
$\frac{215}{934}$
Solution
Total number of ball in the bags $= 6 + 8 + 5 = 19$
P = $\frac{n(E)}{n(S)}$ =
n(E) = $^{6}{{C}_{2}}{{\times }^{13}}{{C}_{1}}~{{+}^{6}}{{C}_{3}} = 195 + 20 = 215$
n(S) = $^{19}{{C}_{3}}=\frac{!19}{!3\times !19-3}=~\frac{19\times 18\times 17}{3\times 2\times 1}=19~\times 3\times 17=969$
P = $\frac{215}{969}$