When five standard six-sided dice are rolled sequentially there are 6^5 = 7776 possible outcomes. For how many outcomes is the sum of the five rolled numbers exactly 27?
36666 , 45666 , 46566 , 46656 , 46665 , 54666 , 55566 , 55656 , 55665 , 56466 , 56556 , 56565 , 56646 , 56655 , 56664 , 63666 , 64566 , 64656 , 64665 , 65466 , 65556 , 65565 , 65646 , 65655 , 65664 , 66366 , 66456 , 66465 , 66546 , 66555 , 66564 , 66636 , 66645 , 66654 , 66663 , Total = 35 such outcomes.
