Irish Lotto Draws

how would you work out this?

i do a treble on the irish lottery in a bookies and i want to know the chance of winning and how it is worked out as i cant figure it out myself.

there are 45 balls total with 6 being drawn (7 including the bonus ball) I only pick 3 numbers and need all 3 to come out to win (it is not like the normal lotto where u pick 6 numbers)

i want to know how to actually work this out and find out my actual chance of winning firstly without the bonus ball (6 balls drawn) and then with the bonus ball (the way this bet works the bonus ball is simply counted as an extra number so it is like the are 7 balls drawn and i need 3 of them to be the 3 i pick to win)

i hope i explained the question well enough, thanks

The first number has a 1 in 45 chance of coming out, so the odds then are 1/45. The second has a one in 44 chance. So- 45 X 44 = 1980. The third has a one in 43 chance of coming out, 1980X43= 85140.

As there are seven balls and you only need three, 7X6X5 will give you the possible permutations and it’s 210.To get the permutations with the bonus ball, multiply by 4 (4 balls) and that’s 840.

This gives you just under a one per cent chance of a win, but it’s still better than the National Lottery.