**PART 2) (medium)** in a lotto where you are eligible to win multiple prizes (eg if you win 1st division you also win a certain amount of 2nd division, 3rd division etc) do you need to include the probability of winning higher prizes when trying to calculate return?

eg:

take a standard lotto with 6 balls chosen from 38. the formula for each number of correct picks is (k,b)(n-k,k-b)/(n,k)

here is the expectancy table:

correct | | probability | | odds | | | prize | return |

6 | | 3.6223E-07 | | 2,760,681 | | | 20,000 | 0.007245 |

5 | | 6.9548E-05 | | 14,379 | | | 1,000 | 0.069548 |

4 | | 0.00269499 | | 371 | | | 100 | 0.269499 |

3 | | 0.03593316 | | 28 | | | - | 0 |

2 | | 0.19538657 | | 5 | | | - | 0 |

1 | | 0.43766592 | | 2 | | | - | 0 |

| | | | | | | | 0.346291 |

the question is for eg calculating the return for the '5 correct' scenario, do i need to also add the probability that i could get all 6 correct? or is that already considered in the formula =COMBIN(6,5)*COMBIN(38-6,6-5)/COMBIN(38,6)