A bit simple for you this but please help....

.... Its been forever since I looked at this sort of problem and I had to use Excel to calcualte the answer which really annoyed me as I seem to recall a simpler process. The problem was thus:

"A sultan has 14 children. He chooses to read a fairy tale to 4 children each night. How many combinations of 4 children are there without repeating any combination. I.E. How many nights will that one fairytale last?"

As said, I got the answer, but used Excel to do it - please would somebody help me with a more technical way of attacking this problem.


Many thanks.
Surtism

Originally posted by Surtism
.... Its been forever since I looked at this sort of problem and I had to use Excel to calcualte the answer which really annoyed me as I seem to recall a simpler process. The problem was thus:

"A sultan has 14 children. He chooses to read a fairy tale to 4 children each night. How many combinations of 4 children are there without repeating any combina ...[text shortened]... mebody help me with a more technical way of attacking this problem.


Many thanks.
Surtism

I believe the formula you seek is

C(n,r) = (n!)/(r!*(n-r)!)

C(n,r) the number of combinations of "n" distinct objects taken "r" at a time.

so your problem

C(14,4) = 14!/(4!*(14-4)!)

= (14*13*12*11*10!)/(4!*10!)

=(14*13*12*11)/(4*3*2*1)

=1001 days

Originally posted by Surtism
.... Its been forever since I looked at this sort of problem and I had to use Excel to calcualte the answer which really annoyed me as I seem to recall a simpler process. The problem was thus:

"A sultan has 14 children. He chooses to read a fairy tale to 4 children each night. How many combinations of 4 children are there without repeating any combina ...[text shortened]... mebody help me with a more technical way of attacking this problem.


Many thanks.
Surtism

I don't quite follow your statement, "i.e. How many nights will that one fairytale last?"

If the requirement is that each child can only hear the fairytale once, then there is simply 14/4 = 3.5 ~= 4 nights that the fairytale will last.

If you did every combination, every child would hear the fairytale multiple times.

^ Interactive tale perhaps.

Originally posted by joe shmo
I believe the formula you seek is

C(n,r) = (n!)/(r!*(n-r)!)

C(n,r) the number of combinations of "n" distinct objects taken "r" at a time.

so your problem

C(14,4) = 14!/(4!*(14-4)!)

= (14*13*12*11*10!)/(4!*10!)

=(14*13*12*11)/(4*3*2*1)

=1001 days

Thanks very much, so in simple terms:

4/14 x 3/13 x 2/12 x 1/11 = 1/1001


How would it work for the probability of getting 3 numbers on the UK lottery?

Originally posted by Surtism
Thanks very much, so in simple terms:

4/14 x 3/13 x 2/12 x 1/11 = 1/1001


How would it work for the probability of getting 3 numbers on the UK lottery?

ahhh...i think you just replace "n" with how many numbers are on the ticket, and "r" would be "3" for your particular situation....

I get

49!/(3!*(49-3)!)=18424

so 1/18424

I could be wrong.