In the finale of the Indian Idol programme, Ladies Special, there are four women contestants - Arunima, Priyamani, Razi and Shriya. The organisers send all participants a list of $7$ songs, asking each one to pick one song for the finale. All the four girls pick the same song, Pyar Hua Chupkese from the film ${1942}$ A Love Story. To resolve the tie, two days before the finale, the organisers prepare $7$ sheets of paper and fold them. Exactly one of the $7$ songs from the list is written on each folded sheet and the folded sheets are identical in all other aspects. First Arunima is asked to pick one sheet out of $7,$ then Priyamani is asked to pick one sheet out of the remaining $6,$ then Razi is asked to pick one out of the remaining $5$ and finally Shriya is asked to pick one out of the remaining $4.$
- What is the probability that the sheet chosen by Razi has the song Pyar Hua Chupkese?
- When Shriya is asked to choose a sheet, she argues that the three sheets chosen by the others should be opened, and if Pyar Hua Chupkese is not chosen by anyone, she should be allowed to pick that song. This is agreed to. What is the probability that Shriya gets to sing the song Pyar Hua Chupkese?
