How do you work out this question?

#1
Hi,

I am intrigued by this intriguing question. Kindly advise on how this can be worked out!

PS - please only take this as an academic question.

A lottery draws 6 winning numbers from 1 to 49.

What’s the most cost efficient option to draw all 6 winning numbers, i.e. which option has the highest probability per dollar to draw all 6 winning numbers?

Cost | Description

$1 | The computer to select 6 number at random.

$1 | you select 6 numbers from 1 to 49.

$7 | you select 7 numbers from 1 to 49.

$28 | You select 8 numbers from 1 to 49.

$84 you select 9 numbers from 1 to 49.

$210 | You select 10 numbers from 1 to 49.

$462 | you select 11 numbers from 1 to 49.

$924 | you select 12 numbers from 1 to 49.

$44 | You select 5 numbers from 1 to 49. The 6th number is any of the guaranteed winning numbers.