问题 填空题

将6本不同的书分给甲、乙、丙、丁4个人,每人至少一本的不同分法共有______种.(用数字作答)

答案

先把6本不同的书分成4组,每组至少一本.

若4个组的书的数量按3、1、1、1分配,则不同的分配方案有

C36
=20种不同的方法.

若4个组的书的数量分别为2、2、1、1,则不同的分配方案有

C26
?C24
2!
?
C12
?C11
2!
 45种不同的方法.

故所有的分组方法共有20+45=65种.

再把这4组书分给4个人,不同的方法有65

A44
=1560种,

故答案为 1560.

单项选择题
填空题

President Bush arrived in Washington and forged ahead with an ambitious agenda- (1) tax cuts, vast changes in federal social programs, expansions of executive power and (2) broad remaking of energy and education policies.
Claiming a mandate by simply declaring (3) existence, his early successes dazzled his critics. With guru Karl Rove directing the (4) , Bush won a stunning series of political victories.
He muscled his agenda through (5) friendly Congress, and gained seats for his party in the 2002 midterm elections. (6) biggest triumph came in 2004, when he won a second term despite a (7) unpopular war.
The "permanent" Republican majority he and Rove envisioned even seemed attainable (8) Bush plunged himself into his most ambitious legislative effort yet: a partial privatization (9) Social Security.
But the president who boasted about "political capital" in the heady (10) after his re-election now faces the worst of political fates as he enters (11) final year in office: borderline irrelevance.
The president’s second term has (12) defined by legislative paralysis, marked by record-low approval ratings, presidential candidates who are (13) from his shadow, and a lingering war that’s sapping his remaining reservoirs of (14) .
As he enters his final year in office with the war continuing, Republican (15) for president bolting from his shadow, and his party back in the minority (16) Congress, he is politically weakened, an early entry into lame-duck status.
And the (17) Washington atmosphere he hoped to cure is just as nasty as it was (18) he came to office seven years ago.
"lie’s left our political institutions much (19) troubled than they were before," said Thomas E. Mann, a senior fellow at (20) Brookings Institution, a Washington-based think tank. "He didn’t create the ideological polarization, but he magnified it. \