Answer to Question #326179 in Statistics and Probability for Robera

Question

Among 15 clocks there are two defectives. In how many ways can an inspector chose

three of the clocks for inspection so that:

a. There is no restriction.

b. None of the defective clock is included.

c. Only one of the defective clocks is included.

d. Two of the defective clock is included.

Answer 1

a.$C^3_{15}=\frac{15!}{12!3!}=455$

b.$C^3_{15-2}=\frac{13!}{10!3!}=286$

c. $C^1_2C^2_{13}=\frac{2!}{1!1!}\frac{13!}{11!2!}=156$

d.$C^2_2C^1_{13}=1\cdot\frac{13!}{12!1!}=13$