Let S = {1,2,3,4,5}

(a) List all the 3-permutations of S

(a) List all the 3-combinations of S

Can any one help me with this ??

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- Nov 17th 2008, 09:29 AMbhuvanCounting problem
Let S = {1,2,3,4,5}

(a) List all the 3-permutations of S

(a) List all the 3-combinations of S

Can any one help me with this ?? - Nov 17th 2008, 11:12 AMTitaniumX
a) 5C3 = 5!/(3!*(5-3)!) = 10 (order doesn't matter)

b) 5P3 = 5!/(5-3)! = 60 (order matters)

a)

{1,2,3}

{1,2,4}

{1,2,5}

{1,3,4}

{1,3,5}

{1,4,5}

{2,3,4}

{2,3,5}

{2,4,5}

{3,4,5}

Total = 10

b)

{1,2,3}

124

125

132

134

135

142

143

145

152

153

154

.

.

.

should add up to 60 - Nov 17th 2008, 12:33 PMSoroban
Hello, bhuvan!

Quote:

Let $\displaystyle S \:=\: \{1,2,3,4,5\}$

(a) List all the 3-permutations of $\displaystyle S $

I'll start the list . . .

. . $\displaystyle \begin{array}{cccccccccccc}

123 & 124 & 125 & 132 & 134 & 135 & 142 & 143 & 145 & 152 & 153 & 154 \\ \\[-4mm]

213 & 214 & 215 & 231 & 234 & 235 & 241 & 243 & 245 & 251 & 253 & 254 \\ \\[-4mm]

312 & 314 & 315 & 321 & 324 & 325 & 341 & 342 & 345 & 351 & 352 & 354 \\

& & & & \hdots & \text{etc.} & \hdots\end{array}$

Quote:

(b) List all the 3-combinations of $\displaystyle S$

. . $\displaystyle \begin{array}{ccccc}(1,2,3)&(1,2,4)&(1,2,5)&(1,3,4 )&(1,3,5) \end{array}$ . $\displaystyle \begin{array}{ccccc}(1,4,5)&(2,3,4)&(2,3,5)&(2,4,5 )&(3,4,5) \end{array}$

Edit: . Ha! TitaniumX beat me to it . . .

. - Nov 17th 2008, 01:58 PMbhuvan
thank you very much ...

How many solutions are there to the equation

x1+x2+x3+x4=17

where x1,x2,x3 and x4 are nonnegative integers ??

appreciate your reply. - Nov 17th 2008, 02:24 PMPlato
- Nov 17th 2008, 04:10 PMbhuvan
can you please give me one example of that ??