Tab  Yahoo  - , , Hits: 564


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1) .

:

(a1,a2,,an) (b1,b2,,bm),

I- n , II- m , w = (ai, bj), i=[1;n], j=[1;m] n*m, .. |W| = n*m

r :

(a1,a2,,an1) ( n1 ),

(b1,b2,,bn2) ( n2 ),

(1,2,,n3) ( n3 ),

(x1,x2,,xnr) ( nr ),

.. - w = (ai1,bi2,,xir), i1 = [1;n1]; i2 = [1;n2]; ir = [1;nr],

..

|W| = n1*n2**nr

.

r . n1 , n2 , n3 .. r- , nr , r



n1* n2* n3** nr .

, .

, n1 = 3, n2 = 2, n3 = 2:

n2 1 n3

1

n1 2

1 1

2

2

1

1

2

0 2

2 1

2

1

1

2

3

2 1

2

n1 * n2 * n3 = 3 * 2 * 2 = 12

1

, . , , , , . ?

, .. 2 , 25 = 32 , , , .

2) .

, m , n , - n+m .

2

1,2,3,4,5 , . , ?

( i1i2i3 ), (i1i2i3i4) (i1i2i3i4i5). ( ) 5*4*3, 5*4*3*2, 5*4*3*2*1. 5*4*3 + 5*4*3*2 + 5*4*3*2*1 = 300.

3) .

, r n (, , .. M=(1,2,,n)), r n. n ?

w = (i1, i2,,ir), ij , j- , j=1,2,,r. .


|W| = n * (n-1)(n-2)(n-r+1) = = = (n)r

 

 

 

 

1

n M=(1,2,,n) r (i1,,ir) M. (i1,,ir) (j1,,jr) , ik = jk, k=[1;r].

= , = 1 (0!=1)

3

10 ?

:

10 , 9 , 8 , 7 ,

|W| = 10*9*8*7 = = 10!/6!

4) .

2

n M = (1,2,,n) n M n.

w=(i1,i2,,in) n . n

n = n*(n-1)*(n-2)**3*2*1 = n!

3

10!=10 .

5) .

n r (rn) , , w=(i1,i2,,ir), i1<i2<<ir, ij , j= [1;r]. r! , . r n

|W| = / r! = = = () (rn)

n r.

, .

3

n M = (1,2,,n) r , r .

, .



:

= , ==1, = + (1 r n) ( )

(a+x)n = ar xn-r.

. a=x=1 ޠ = 2n.

= , r=0,1,,n.

4

4 , ,

) : 4 10;

) : ;

) : ;

) D: .

:

,

) |A| = ;

) |B| = * ;

) |C| = * 24;

) |D| = 5 * * 22.

6)

n n1 n2 = n-n1 , n

|W| = = =

, , n n1 I- , , n2 = (n-n1) II- .

5

) , 1 1 1 1 7 7 7?

: = = ,

) 1?

:

4 1 3 7 , 3 7?

|A| =

n=3 r=4

n 1 r 7

,

n , n1 , n2 , n3 .. nk k- , . n

|W| = , ( * )

n1+n2+n3++nk = n.

n1 n , n2 n-n1 .. nk k- ,

|W| = =

= =

= .

6

?

:

(*)

|W| = .

7) .

, n , r , . (k1, k2,,kn), ki i- , i=[1;n], k1+k2++kn = r, ki .

|W| = .

, (k1, k2,,kn) * |

*** | **** | | *****

k1 k2 kn

* k1+k2++kn = r, | n-1, . * | n+r-1, r *, n-1 |.

r * n-1 | , * |. r * n+r-1 . *, |. r * n-1- | . n+r-1 n-1 |, , | , * , = , .

7

: n=7, r=2, |W| = = 28, : n=7, r=3, |W| = =84.

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