Three numbers are selected from the set {1, 2, 3, …., 23, 24}, with out replacement. The probability that the formed numbers from an A.P. is equal to
Answer & explanation
Correct answer: option 3
Let the selected numbers be n1, n2 and n3.
We must have
2n2 = n1 + n3
Thus n1 + n2 must be even. That means n1 and n3 both must have same nature.
Thus, required probability = $\frac{2 .^{12} C_2}{{ }^{24} C_3}=\frac{3}{46}$