How many integers between 100 and 800 have three different digits in increasing order? One such integer is 129.
\(\phantom{100 and 150}\)
123 , 124 , 125 , 126 , 127 , 128 , 129 , 134 , 135 , 136 , 137 , 138 , 139 , 145 , 146 , 147 , 148 , 149 , 156 , 157 , 158 , 159 , 167 , 168 , 169 , 178 , 179 , 189 , 234 , 235 , 236 , 237 , 238 , 239 , 245 , 246 , 247 , 248 , 249 , 256 , 257 , 258 , 259 , 267 , 268 , 269 , 278 , 279 , 289 , 345 , 346 , 347 , 348 , 349 , 356 , 357 , 358 , 359 , 367 , 368 , 369 , 378 , 379 , 389 , 456 , 457 , 458 , 459 , 467 , 468 , 469 , 478 , 479 , 489 , 567 , 568 , 569 , 578 , 579 , 589 , 678 , 679 , 689 , 789 , Total = 84 such 3-digit integers.
