I need some help in solving a math problem!

[frank mccune]

    Hi:  To Howard and all of the other smart people out there:

     In 1973 I ordered a Heathkit Thumb Tac kit.  When it arrived I began to pull the parts out of the shipping container, I noticed that I had removed package numbered one.  These parts were all jumbled together in no order in the box.  They were in a random mix that was loose in this box.

     Upon reaching into the box the second time, I picked out part number two.  This went on in order on each reach into the box of parts.  Every reach into the box, I came out with the correctly numbered part that conincided with the number of times that I had reached into the box.  This was done each time for all 24 parts.  I was 24/24!

     Now my question is this.   What is the probability that I could match the number of reaches into the box of parts with the correct number on the part?

    Any help in solving this probility question?

                                                                                                 Tia,

                                                                                                 Frank

[Tim Wescott]

Frank, you were almost certainly playing with a stacked deck.  Someone put #24 in first, then #23, etc.

If everything were completely random, then the chances that you'd pull the correct part on the first draw was 1 in 24 -- 1/24 in Math.  Then the chances that you'd pull the next correct part on the second draw was 1 in 23 ('cause now there's 23 parts left in the box) or 1 in 23.  The probability SO FAR of getting it right is 1 in (24)(23).  Keep doing that, and when you're done the probability is 1 in (24)(23)(22) ... (2)(1) (always remember to multiply by one at the end -- it gives you a feeling of confidence that's always unwarrented, but on some days can be very comforting).

The number (n)(n-1)(n-2)...(2)(1) is special -- it's called "n factorial", and noted as "n!"  I'm not sure why they chose '!' -- perhaps because n! grows so astonishingly fast.

At any rate, 24! is a bit more than 6.2 x 10²³, or in English 620 sextillion (I had to look up "sextillion".  It's big.  Almost as big as a bazzilion, which is a system's engineering term for "bigger than you can imagine, but not quite infinite").  To put that into context, if you started doing that experiment today with truly randomized boxes of stuff, then on average you could expect the sun to have gone out and possibly the entire universe to have gone dark before you hit the jackpot and got a perfect draw (assuming, of course, than you hadn't gotten bored and quit yet).

[Howard Rush]

I had to look up "sextillion".  It's big.

It is in the case of the Jive Combat Team.

[frank mccune]

    Hi Tim and Howard:

    Thanks for the imput!

     I now remember that I was shown how to do these types pf problems earlier in life.  My roommate in college who was a math major, explained it all to me years later but I forgot how to do it until you jogged my memory.

     No, the deck was not stacked.  All parts were in a large box in a random manner.  I had two witnesses at the time.  The one would become the class valedictorian of his class in a few months.

       I remember the time that a lady mat 21 straight passes at craps one evening.  Not knowing anything about craps, I was not impressed.  I guess that it was a big deal at the time.  I think that that record has been broken.  Something to research on Goggle.

      A while back I was looking through a fifth grade book about Probability and I got lost attempting to understand that material! Lol  Needless to say, I have not had much experience in math!

                                                                                                         Stay well my friends,

                                                                                                          rank

[Rafael Gonzalez]

Frank, you were almost certainly playing with a stacked deck.  Someone put #24 in first, then #23, etc.

If everything were completely random, then the chances that you'd pull the correct part on the first draw was 1 in 24 -- 1/24 in Math.  Then the chances that you'd pull the next correct part on the second draw was 1 in 23 ('cause now there's 23 parts left in the box) or 1 in 23.  The probability SO FAR of getting it right is 1 in (24)(23).  Keep doing that, and when you're done the probability is 1 in (24)(23)(22) ... (2)(1) (always remember to multiply by one at the end -- it gives you a feeling of confidence that's always unwarrented, but on some days can be very comforting).

The number (n)(n-1)(n-2)...(2)(1) is special -- it's called "n factorial", and noted as "n!"  I'm not sure why they chose '!' -- perhaps because n! grows so astonishingly fast.

At any rate, 24! is a bit more than 6.2 x 10²³, or in English 620 sextillion (I had to look up "sextillion".  It's big.  Almost as big as a bazzilion, which is a system's engineering term for "bigger than you can imagine, but not quite infinite").  To put that into context, if you started doing that experiment today with truly randomized boxes of stuff, then on average you could expect the sun to have gone out and possibly the entire universe to have gone dark before you hit the jackpot and got a perfect draw (assuming, of course, than you hadn't gotten bored and quit yet).

6.20448401733239439360000   CLOSE...

I BUILT A HEATHKIT RADIO ~ 1978!! In those days they used 27 MHZ but I got it after they opened the 72-75 MHZ band. Got 5 servos also. All of Heathkit's R/C components were made by Kraft!!! OHHH I am getting nostalgic...