+100 Catherine rolls a 6-sided die five times, and the product of her rolls is 300. How many different sequences of rolls could there have been? (The order of the rolls matters.)
There are this many sequences of rolls to obtain a product of 300:
12556 , 12565 , 12655 , 13455 , 13545 , 13554 , 14355 , 14535 , 14553 , 15256 , 15265 , 15345 , 15354 , 15435 , 15453 , 15526 , 15534 , 15543 , 15562 , 15625 , 15652 , 16255 , 16525 , 16552 , 21556 , 21565 , 21655 , 22355 , 22535 , 22553 , 23255 , 23525 , 23552 , 25156 , 25165 , 25235 , 25253 , 25325 , 25352 , 25516 , 25523 , 25532 , 25561 , 25615 , 25651 , 26155 , 26515 , 26551 , 31455 , 31545 , 31554 , 32255 , 32525 , 32552 , 34155 , 34515 , 34551 , 35145 , 35154 , 35225 , 35252 , 35415 , 35451 , 35514 , 35522 , 35541 , 41355 , 41535 , 41553 , 43155 , 43515 , 43551 , 45135 , 45153 , 45315 , 45351 , 45513 , 45531 , 51256 , 51265 , 51345 , 51354 , 51435 , 51453 , 51526 , 51534 , 51543 , 51562 , 51625 , 51652 , 52156 , 52165 , 52235 , 52253 , 52325 , 52352 , 52516 , 52523 , 52532 , 52561 , 52615 , 52651 , 53145 , 53154 , 53225 , 53252 , 53415 , 53451 , 53514 , 53522 , 53541 , 54135 , 54153 , 54315 , 54351 , 54513 , 54531 , 55126 , 55134 , 55143 , 55162 , 55216 , 55223 , 55232 , 55261 , 55314 , 55322 , 55341 , 55413 , 55431 , 55612 , 55621 , 56125 , 56152 , 56215 , 56251 , 56512 , 56521 , 61255 , 61525 , 61552 , 62155 , 62515 , 62551 , 65125 , 65152 , 65215 , 65251 , 65512 , 65521 , Total = 150 such sequences.
