Table Method with Six Tiles
(Grades 7-8)
(Listing all of the possible 3-number combinations that can
be drawn; highlighting the outcomes of 7.)
There
are 216 possible 3-number (3-draw number) combinations. Of these 216 possible three-draws, 27 end up
with an outcome of 7 (i.e., the two highest numbers add to 7). The possibility of obtaining an outcome of 7
is 27/216 or 1/8.
111 112 113 114 115 116 |
211 212 213 214 215 216 |
311 312 313 314 315 316 |
411 412 413 414 415 416 |
511 512 513 514 515 516 |
611 612 613 614 615 616 |
121 122 123 124 125 126 |
221 222 223 224 225 226 |
321 322 323 324 325 326 |
421 422 423 424 425 426 |
521 522 523 524 525 526 |
621 622 623 624 625 626 |
131 132 133 134 135 136 |
231 232 233 234 235 236 |
331 332 333 334 335 336 |
431 432 433 434 435 436 |
531 532 533 534 535 536 |
631 632 633 634 635 636 |
141 142 143 144 145 146 |
241 242 243 244 245 246 |
341 342 343 344 345 346 |
441 442 443 444 445 446 |
541 542 543 544 545 546 |
641 642 643 644 645 646 |
151 152 153 154 155 156 |
251 252 253 254 255 256 |
351 352 353 354 355 356 |
451 452 453 454 455 456 |
551 552 553 554 555 556 |
651 652 653 654 655 656 |
161 162 163 164 165 166 |
261 262 263 264 265 266 |
361 362 363 364 365 366 |
461 462 463 464 465 466 |
561 562 563 564 565 566 |
661 662 663 664 665 666 |
(Determining the possible 3-number combinations by
calculation;
determining the number of outcomes of 7 by reasoning and
calculating.)
Total
number of 3-number combinations possible:
6
x 6 x 6 216
This
is because there are 6 possible numbers for the first tile, each of which can be
followed by 6 possible numbers for the second tile. These 36 pairs can each be followed by 6 possible numbers for the
third tile. This makes a total of
36 x 6 = 216 combinations total.
Total
number of outcomes of 7 possible:
The
possible combinations of 3 numbers that could be combined to get a 7 from the
highest two draws are:
611 (No other higher numbers would work with a
6; only 6 and 1 equal 7.0
522 (No other higher numbers would work with the
5; only 5 and 2 followed by 2 or 1.)
521 (See above.)
433 (No other higher numbers would work with the
4; only 4 and 3 followed by 3, 2, o4 1.)
432 (See above.)
431 (See above.)
Starting
with a 3, 2, or 1 would result in the same groups of 3 numbers already listed,
only in different order.
These
6 trios of numbers can, now, be accomplished in different orders, as follows:
611: 611, 161, 116 (3
ways)
522 522,
252, 225 (3
ways)
521: 521, 512, 251, 215,
152, 125 (6
ways)
433: 433, 343, 334 (3
ways)
432: 432,
423, 342, 324, 243, 234 (6
ways)
431: 431, 413, 341, 314,
134, 143 +
(6 ways)
27
ways
Out
of the 216 possible 3-number combinations (tiles draws), 27 will result in an
outcome of 7. 27/216 or 1/8
is the probability of obtaining an outcome of 7.