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

 


 

Alternative Method - Grades 7-8

(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.