Question

Permutations/Combinations:
A coin is tossed 20 times and the heads and tails sequence is recorded. From among all the possible sequences of heads and tails, how many have exactly seven heads?

Answer 1

it's just a combination:
20 choose 7 = 20C7\[\left(\begin{matrix}20 \\7 \end{matrix}\right)\]
\[\frac{ 20! }{ (20-7)!7! }\]
\[\frac{ 20! }{ 13! 7! }\] = 77,520

Answer 2

Oh, i understand it a bit better now. I put 40 instead of 20 because I thought it flipped 20 times and there are 2 heads..and multiply...it doesn't really make sense. Thanks for your hlep!

Answer 3

Remember this equation.
\[\left(\begin{matrix}n \\ r\end{matrix}\right)\]
or
\[_{n} C _{r}\]
Formula:
\[\frac{ n! }{ r!(n-r)! }\]

Answer 4

also, does "different" mean a permutation?

Answer 5

different combinations?

Answer 6

like for example, How many DIFFERENT license plates consist of five symbols, either digits or letters? Would that be a permutation?

Answer 7

differrent means number of combinations.

Answer 8

Permutation is used to find the different combinations.

Answer 9

in general try to think of permutations as being used when order matters and combinations when order doesn't
the license plate example is a permutation because you have a choice of symbols for each ordered position:
ex.: 3 letters then 3 numbers --> # of possibles = 26*26*26*10*10*10
the standard example for combinations is for choosing committee members i.e. a committee of Peter and Mary is no different than a one of Mary and Peter; a permutation would doubly count this. that why combinations have another factor in the denominator to divide by to correct for this.
perm. = n!/(n-r)! and combin. = n!/((n-r)!*r!)
if the license plate was a combination then ABC123 would be no different then B21CA3 or any other arrangement of the characters