Each lottery ticket buyer was assigned a sequence of 3

Question

Each lottery ticket buyer was assigned a sequence of 3 different integers from the set of integers 1 through 8. If no equence was assigned to more than one participant and if 20 of the possible sequnces were not assigned, what was the number of of buyers? (EX, the sequence 1,2,3 is different from the sequence 3,2,1)

lhotseface · Answer

492 ?

Since each of the numbers can have 8 values. The total number of events is the multiplication of independent events = 8*8*8 = 512. 
512 - seq. not assigned = 512 - 20 = 492 which is the number of buyers.

ps_dahiya · Answer

We have eight numbers. In how many ways we can arrange these number selecting only three numbers with no number repeatition.

= 8P3 = 8 * 7 * 6 = 336

Total buyers = 336-20 = 316

giddi77 · Answer

Each digit can be occupied by 8 values. Need to subtract 20 from the answer = 8*8*8 - 20 = 492

ps_dahiya · Answer

I don't know where I read "no digits are repeated". :roll:

Yes it should be 8 * 8 * 8 -20 = 492

5elements · Answer

ps_dahiya, I am thinking your first answer was right, i.e 8P3-20, because the question says "a sequence of 3 different integers " meaning no repeats :!:

pmenon · Answer

hmmmm .... a sequence of 3 different integers. I would take that to mean that numbers wont be repeated.

ps_dahiya, then you were initially correct by doing ( 8x7x6 ) - 20.

ps_dahiya · Answer

Wow, I am now paying attention to minute details. :-D

giddi77 · Answer

Way to go buddy. :good

Just maintain the same for 4.5 hrs on your G-day and you will be atleast on the 7th heaven!

joemama142000 · Answer

the oa is

(8*7*6)-20

My question is how do you know when to use the combo or perm formula? I know that combo order doesnt matter, perm order matters. How do you know the order matters here? what gives it away? thanks!

ywilfred · Answer

In this case, order matters, because the numbers 2-8 will be taken three at a time to form a unique lottery number. So 123 will be different from 321, 231, 312 etc. In another words, buying the lottery number 123 doesn't mean that you have stuck if the winning number is 321.

Cases where you use combination are instances that does not invovle any form of arrangement. For example, out of eight people, how many 3 people teams can be formed. So if you have A,B,C,D,E,F,G,H a team comprising of ABC is the same as a team comprising of BCA. 

However, if you have an instance like the three man team is used to fill the positions of president, vice-president and secretary, then it is another story altogether. Now you need to consider permutations as order comes into the picture. A team that has A as president, B as vice-presisdent and C as secretary is not the same as B being the president, C being the vice-president and A being the secretary, this despite the fact both teams comprise of A,B and C.

Each lottery ticket buyer was assigned a sequence of 3

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