## lookitswill 2 years ago 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?

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1. Tolio

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

2. lookitswill

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!

3. Azteck

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

4. lookitswill

also, does "different" mean a permutation?

5. Azteck

different combinations?

6. lookitswill

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

7. Azteck

differrent means number of combinations.

8. Azteck

Permutation is used to find the different combinations.

9. Tolio

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