Question

A technician is launching fireworks near the event of a show. Of the remaining 11 fireworks, 4 are blue and 7 are red. If she launches 6 of them what’s the probability that 2 of them will be blue

Answer 1

$\displaystyle |\Omega|=\binom{11}{6}=\dfrac{11!}{6!5!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\ |A|=\binom{4}{2}=\dfrac{4!}{2!2!}=\dfrac{3\cdot4}{2}=6\\\\ P(A)=\dfrac{6}{462}=\dfrac{1}{77}\approx1\%$