- #1
threeder
- 27
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Homework Statement
1. Three people each select a different card from a single pack of 52 distinct cards. How mnay choices are possible if we record who selected which card, and if we forget who selected which card?
2. Three people each select a main dish from a menu of five items. How many choices are possible if we record who selected which dish and if we ignore who selected which dish?
3. Use [itex] (1+i)^n[/itex] to prove that [tex]{\sum_{0\geq 2r\geq n}} (-1)^r \binom{n}{2r} = \begin{cases}(-4)^k = 0 &if ~n=4k,\\(-4)^k = 0 &if ~n=4k+1,\\0 &if ~n=4k+2,\\ \frac{1}{2}(-4)^{k+1} = 0 &if ~n=4k+3,\end{cases}[/tex]
The Attempt at a Solution
Just want to make sure that I got first two right:
1. If we record who selected - 132600 and three times more if we forget.
2. If we record who selected - 125 and three time more if we forget
3. As for the third I am stuck. Tried to plug different values for n, but then got lost in algebra. I think there has to be a better way using the hint as well, right?