Question

student is to match three historical events (Mahatma Gandhi’s Birthday, India’s freedom, 

and First World War) with three years (1947, 1914, 1896). If he guesses with no knowledge 

of the correct answers, what is the probability of the number of answers he gets correctly?

Answer 1

$The\,\,student\,\,needs\,\,to\,\,put\,\,the\,\,events\,\,1,2,3 in\,\,the\,\,correct\,\,order.\\X-the\,\,number\,\,of\,\,correct\,\,answers\\All\,\,possible\,\,variants\,\,are\\\left( 1,2,3 \right) ,X=3\\\left( 1,3,2 \right) ,X=1\\\left( 2,1,3 \right) ,X=1\\\left( 2,3,1 \right) ,X=0\\\left( 3,1,2 \right) ,X=0\\\left( 3,2,1 \right) ,X=1\\P\left( X=0 \right) =\frac{2}{6}=\frac{1}{3}\\P\left( X=1 \right) =\frac{3}{6}=\frac{1}{2}\\P\left( X=3 \right) =\frac{1}{6}\\$