Table Method with Four Tiles (Grades 5-6)

(Listing all of the possible 3-number combinations that can be drawn; highlighting the outcomes of 5.)

There are 64 possible 3-number (3-draw number) combinations.  Of these 64 possible three-draws, 12 end up with an outcome of 5 (i.e., the two highest numbers add to 5).  The possibility of obtaining an outcome of 5 is 12/64 or 3/16.

 111 112 113 114 211 212 213 214 311 312 313 314 411 412 413 414 121 122 123 124 221 222 223 224 321 322 323 324 421 422 423 424 131 132 133 134 231 232 233 234 331 332 333 334 431 432 433 434 141 142 143 144 241 242 243 244 341 342 343 344 441 442 443 444

# Alternative Method

(Determining the possible 3-number combinations by calculation;

determining the number of outcomes of 5 by reasoning and calculating.)

Total number of 3-number combinations possible:

4 x 4 x 4  = 64

Total number of outcomes of 5 possible:

The possible combinations of 3 numbers that could be combined to get a 5 from the highest two draws are:

These 6 trios of numbers can, now, be accomplished in different orders, as follows:

411:  411, 141, 114                                                                             (3 ways)

322:  322, 232, 223                                                                             (3 ways)

321:  321. 312, 231, 213, 123, 132                                                + (6 ways)

12 ways

Out of the 64 possible 3-number combinations (tiles draws), 12 will result in an outcome of 5.  12/64  or 3/16  is the probability of obtaining an outcome of 5.