Question

If 5 balls are picked at random, what is the probability that none are orange ?

• A. $\frac{33}{442}$
• B. $\frac{442}{33}$
• C. $\frac{15}{167}$
• D. $\frac{23}{235}$
• E. $\frac{35}{235}$

Answer 1

The correct option is A $\frac{33}{442}$

${}^{17}{C}_5=17\times 16\times 15\times 14\times \frac{13}{5}\times 4\times 3\times 2\times 1=\frac{742560}{120}=6188{}^{}{}^{11}{C}_5=11\times 10\times 9\times 8\times \frac{7}{5}\times 4\times 3\times 2\times 1=\frac{55440}{120}=462P=\frac{462}{6188}=\frac{33}{442}$