7

(3) �w��p��O�k�͡A�p��O�k�͡A�h�p��Q�⤤��v�j��p��Q�⤤��v

(4) �Y�ǥͥҩM�ǥͤA�b�P�@�Z�A�ǥͤ��b�t�~�@�Z�A�h�ҡB�A��H�P�ɳQ�⤤��

(5) �ǥ�A�M�ǥ�B�O�S�̡A�L�̦P�ɳQ�⤤��v�p�� ${\frac{1}{100}}$ .

��:��D�O�˴��P�ǬO�_�M��ҿסu�H��v��. �H��M��ƾǦU��, ��L��u�H��v��e��y�z, �X�G�S��@�Ӫ��N�H��˩w�q�M��. �P�ǭ̹��H��o�ӷ��i�ೣ�O��``�P��''�B�z, ��D�T��i�˴��X�P�ǭ̹��H��o�ӷ��P��O�_��T, ��L�b�ҥ��L��T�w�q��p�U, �n��T�L�~��ﶵ��ݤ��.

�򥻤W�b 800 �H��H��˩�X 80�H, ��ܳo 800 �H��N 80 �H��զX��i��|�o�ͥB��o�ͪ��|��۵�. ��Ҧ��i�઺�զX��|�o�ͩҥH��i��X�� 80 �H��n�O�Y��Z��P��(��i��|�o�ͥu�O��v�ܧC�Ӥw); �]��i��X��O�k��. �]��ﶵ (1), (2) ��O��. �t�~��Ҧ��i�઺�զX�o�ͪ��|��۵�, �ҥH�ܮe��z�ѨC�ӤH�|�Q�⤤��v��۵�(��k�k)�B��ӤH�Q�⤤��v�]��۵�(��Z�O). �]��ﶵ (3) �O��ӿﶵ (4) �O�諸. �γ\��\�h�P�ǻ{��k�ͤH�Ƥ��h, �Q�⤤��v��M��j, �ӵL�k�z�Ѭ��ﶵ (3) ��. �S��! �k�ͳQ�⤤��v�O��j, ��O�D�جO�n�⤤�S�w��k��p��, �ҥH�b��h��k�ͤ��X�p��v�۹��b�k�ͤ��X�p��v�p. �]��M�e��Ҵ��⤤�k�ͪ��v��⤤�k�ͪ��v�j, ��ۥ��ŬO�|�y��p��M�p��Q�⤤��v�۵�.

�̫�@�ӿﶵ�O�ݩ��v��D, �n�p��P�ɩ⤤ A,B ��H��v. �J�M�O�H��, �C�@�Ӽ˥��I�Q��X��v�ۦP, �ڭ̥i�Υj��v��k�D��v. �]�N�O��X�q 800 �H�� 80 �H��Ҧ��զX�� (�Y 800 $\choose80$ ) �A��q�o 800 �H�� 80 �H��]�t A,B �G�H��Ҧ��զX�� (�ѩ� 80 �H��ݥ]�t A,B �G�H, �o�۷��q 798 �H�� 78 �H, �Y 798 $\choose78$ ). �G�o��v��

$\displaystyle {\frac{\displaystyle{798\choose 78}}{\displaystyle{800\choose80}}}$ = $\displaystyle {\frac{\displaystyle{\frac{798!}{78!720!}}}{\displaystyle{\frac{800!}{80!720!}}}}$ = $\displaystyle {\frac{80\times 79}{800\times 799}}$ < $\displaystyle {\textstyle\frac{1}{100}}$ .

$\displaystyle {\textstyle\frac{80}{800}}$ × $\displaystyle {\textstyle\frac{79}{799}}$ .