Question

During the last class period of the semester, each student in a graduate computer science class with 10 students is required to give a brief report on his or her class project. The professor randomly selects the order in which the reports are to be given. Two students have been working on similar projects and would like to give their reports consecutively. What is the probability that this will happen

Answer 1

Probability = 1/5

Explanation:

Total ways of arrangement for 10 students = 10 !

Ways to arrange 2 students consecutively & other 8 students = 9 ! x 2

( As 9! to arrange 9 units, as 2 considered together ; & 2 for arranging 2 consecutive students - respectively )

So, Probability = Favourable outcomes / Total outcomes

= ( 2 x 9! ) / 10! = ( 2 x 9 x 8 x ..... 2 x 1 ) / 10 x 9 x ....... 2 x 1)

= 2 / 10 = 1/5