In a certain number selection game, the player has to select six unique numbers out of forty ranging from 1 to 40.

The winner is the one who correctly marks the same number combination as generated by a program.

A player is allowed to play only once. We also assume that no two players can select the same combination of numbers.

(i) Determine the probability of winning for a player.

(ii) If a player pays MUR 50 to play and the winner is guaranteed to get MUR 5 000 000, determine the expected gain for the player.

(iii) Suppose there is a second prize of MUR 1 000 000 for any player who selects five out of the six computer-generated numbers. Determine the probability for a player to get a second prize.

(iv) Determine the expected gain for the player-based parts (i) to (iii) above.

(v) Comment on your answers above.