lottery style question

I think I get it but I'm not sure Im doing this right.

on a lottery you can pick 3 of 10 numbers between 0-9 "randomly drawn" the 3 numbers can be the same.

A. what are the odds of getting the 3 numbers, and them being in the same order as drawn.

so I did 10x10x10 because it could be 1/10 3 times so =1000 (correct)

B. this is the one that's giving me trouble.
What are the odds of winning if they can be in any order?
answer is 167.

I know 1000/6 (6 could be 3!) is roughly 167 but I dont know know if thats the right way to do it, or why to do it that way....
I thought it would be 3/10 haha.


I also wanted to know how the two answer's would be changed if they couldnt be the same number. I assume that in part (A) it would be 0x9x8= 1/720 but for part be Im still confused.


thanks.

brentwoodbc said:

on a lottery you can pick 3 of 10 numbers between 0-9 "randomly drawn" the 3 numbers can be the same.
What are the odds of winning if they can be in any order?
answer is 167.

Click to expand...

In this case, the selection [1,4,1] is the same as the selection [1,1,4].
There are \(\displaystyle \binom{3+10-1}{3}=220\) such possible selections.
Where did you get the other answer?

text book.

****straight from text

in a pick 3 lottery, participants pick 3 digits from 0-9 and choose straight or box play.. the lottery corporation randomly selects 3 digits from 0-9. the three digits can be the same. straight play wins if 3 digits picked match the 3 winning digits in the same order, box play wins if if your picks match the winning numbers in any order. According to the lottery corporation, the odds of winning are 1/100 for straight play, and 1/167 for box play. explain how they came to this conclusion.

brentwoodbc said:

in a pick 3 lottery, participants pick 3 digits from 0-9 and choose straight or box play.. the lottery corporation randomly selects 3 digits from 0-9. the three digits can be the same. straight play wins if 3 digits picked match the 3 winning digits in the same order, box play wins if if your picks match the winning numbers in any order. According to the lottery corporation, the odds of winning are 1/100 for straight play, and 1/167 for box play. explain how they came to this conclusion.

Click to expand...

That 'lottery corporation' does not know much about mathematics.
Or maybe it is the author of the textbook.

sorry 1/1000 and 1/167