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 ??
Hello, bhuvan!
There are $\displaystyle _5P_3 \:=\:\tfrac{5!}{2!} \:=\:60$ of them.Let $\displaystyle S \:=\: \{1,2,3,4,5\}$
(a) List all the 3-permutations of $\displaystyle S $
I'll start the list . . .
. . $\displaystyle \begin{array}{cccccccccccc}
123 & 124 & 125 & 132 & 134 & 135 & 142 & 143 & 145 & 152 & 153 & 154 \\ \\[-4mm]
213 & 214 & 215 & 231 & 234 & 235 & 241 & 243 & 245 & 251 & 253 & 254 \\ \\[-4mm]
312 & 314 & 315 & 321 & 324 & 325 & 341 & 342 & 345 & 351 & 352 & 354 \\
& & & & \hdots & \text{etc.} & \hdots\end{array}$
There are $\displaystyle _5C_3 \:=\:\tfrac{5!}{3!2!} \:=\:10$ of them . . .(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 . . .
.