Permutations_and_Combinations.pdf
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Transcript of Permutations_and_Combinations.pdf
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8/14/2019 Permutations_and_Combinations.pdf
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1. F :. ++++ = 20. ++ = 5. 228 . 336 . 448 . 528
2. F + + = 15. 902 . 728 . 734 . 904
3. ABCD 3,4,5,6 AB, BC, CD, DA. :
. 270 . 220 . 282 . 342
4. ,, =24, :. 30 . 60 . 90 . 120
5. 9 . : , . I 4
2 ?
. 1260 . 1280 . 840 . 1920
6. 4 , 5 6 . I ?
. 209 . 210 . 120 . 119
7. 12 A B. I 4 12
?
. 45 . 126 . 84 . 168
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8/14/2019 Permutations_and_Combinations.pdf
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8. (>5). .H .
A: C3 *(4)C1
9. . . F .
A: 126
126
10. . .
, ?
A: (+2)! / (1)!(1)!
11. :
. (7!)2. (6!)2. 6!7! . (7!)2
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8/14/2019 Permutations_and_Combinations.pdf
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1. K (++) >, + = 15. .
16C1
. (++) = 5 7C2
H =16
C1*7C2 = 336
2. : 42+ 2. K = 15 . , . 4*225 + 2 = 902
3. 3C1*4C1*5C1+ 3C1*4C1*6C1+ 4C1*5C1*6C1+ 3C1*5C1*6C1 = 3424. = 24 = 2331
C ,
++ = 3, ++ = 1
=3+31
C31*1+31
C31 = 10*3 = 30
5. 9!/4!2!3! = 12606. 5 0,1,2,3,4
, 6 7 . H 210
. 0 . 2101
= 209 .
7. 1, 2, 3, 4 . 1 2 3 4
, , , , A & 1, 1& 2, . 4& B.
, + + + + = 8
, , . = 9C4 = 126
8. A . :
. H .
H
. H C3.
. H ,
= .
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8/14/2019 Permutations_and_Combinations.pdf
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. H = *
(4)C1
. H = C3 * (4)C1
9. = 12. . 6
= 12*12*12*12*12*12 = 126
6 = 126
, 6 = 126 126
10. . .CA ,
.
11. . I A 6!7!