Question 1149517
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If each gets an odd number of pies, then the numbers of pies are either 1, 3, and 5 (in some order); or 3, 3, and 3.<br>
Give each of the three people his allotment of pies, one person at a time.<br>
(1) First person gets 5 of the 9; second gets 3 of the remaining 4; third gets 1 of the remaining 1.  {{{C(9,5)*C(4,3)*C(1,1) = 126*4*1}}} = 504 ways
(2) First person gets 5 of the 9; second gets 1 of the remaining 4; third gets 3 of the remaining 3.  {{{C(9,5)*C(4,1)*C(3,3) = 126*4*1}}} = 504 ways
(3) First person gets 3 of the 9; second gets 5 of the remaining 6; third gets 1 of the remaining 1.  {{{C(9,3)*C(6,5)*C(1,1) = 84*6*1}}} = 504 ways
(4) First person gets 3 of the 9; second gets 3 of the remaining 6; third gets 3 of the remaining 3.  {{{C(9,3)*C(6,3)*C(3,3) = 84*20*1}}}= 1680 ways
(5) First person gets 3 of the 9; second gets 1 of the remaining 6; third gets 5 of the remaining 5.  {{{C(9,3)*C(6,1)*C(5,5) = 84*6*1}}} = 504 ways
(6) First person gets 1 of the 9; second gets 5 of the remaining 8; third gets 3 of the remaining 3.  {{{C(9,1)*C(8,5)*C(3,3) = 9*56*1}}} = 504 ways
(7) First person gets 1 of the 9; second gets 3 of the remaining 8; third gets 5 of the remaining 5.  {{{C(9,1)*C(8,3)*C(5,5) = 9*56*1}}} = 504 ways<br>
TOTAL: 1680+6(504) = 4704 ways<br>