Dislocation arrangement _1307 -

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Dislocation arrangement

Q. How many different investment law? Solution 1 letter into the mailbox will be only 3 cast method, respectively 2,3. 4, Box, Box 2, if the input is 2, the letter can only be put into 1,3,4 PO Box, 3 and 4, respectively, only one vote in the letter method. . There are 3 × 3 × 1 × 1-9 kinds of investment law. Question 2 of the letter into the number 1,2,3,4.5 number is 1,2. 3,4. 5 mailboxes. Each vote a mail, but letters can not be the same number and mailbox number. Q. How many different investment law? Wrong solution on the problem using methods believed to be 4 1 investment law,[link widoczny dla zalogowanych], if the input box 2. The letter can only be put into 1,3,4.5 2 PO Box. If the 2 letter in the mail 1. There are 2 kinds of 3 letter investment law, Section 4 and 5 of the letters were only one kind of investment law. If the 2 letter in the 3 or 4 or 5,[link widoczny dla zalogowanych], mailbox, then the first 3 letters with 3 vote method. Section 4 and 5,[link widoczny dla zalogowanych], respectively, only one vote in the letter method. Therefore, a total of 4 × (1 × 2X1 × 1 +3 × 3 × 1 × 1) a 44 vote method. If the number of letters and mail more, with each analysis is very complex and prone to error. How will we solve this problem? 2 exploration and discovery are numbered 1,2,[link widoczny dla zalogowanych],3, ..., the letter in the numbered 1,2,3, .... Mailbox. Only vote for each mail a letter to the number of mailbox number can not be the same. How many investment law? The first permutation, there are A: kind of investment method. Only minus the letter should not be cast into the mailbox of the investment law number C · A: b i, but the \. Should be added to A: = l, but with the species, he also added a \. '. And minus C: · II i. ... And so on. Last received: When is even, the total number of investment method A: a A :=;+· A: b; an A: z; + ... a C =-. · A} + C: · Ag; when is odd. Total investment law as a C: · A = b} + · A: b; a A == i + ... + C: -. · A} a C: ·. If the letter h letter with m (≤) can not be put into their mailbox number, the same can be drawn: When is even, the total number of investment law [A: a C2 · A :=}+· b l-C : I · b j + ... a C =: -. · A :=:{{+ C := Kwadratowy

; When is odd, the total number of investment law C7 · [A: A C · A: b} + c2A: b l a ... + ℃: - '· A: =: {} a C: A: b Kwadratowy

. If the provisions of the letter m, the above formula do not need to take before the 02. So many complex problems to be solved. Based on the above discussion, the dislocation can be arranged in the following theorem. Theorem 1 to cut the throat with a number, l the number of inputs to the box numbered 1, each box a number to vote. M in which the number of squares and their number can not be the same, then: when is even, there are A: a C · AT =} + c2-Aj =; a A: = i + ... a C = a Ai + C: · kinds of investment law; 'When is odd, there are A: a c · A: =; + ci. * B l-c: · A: = i + ... + C: -. · A} a cast method. Example 1 day to political, language, mathematics, physics, physical, biological 6 classes, but not on the sports section 1, section II is not on the physical, not on the math section 6, the day of the course there are several permutation? solution obtained using the above formula the number of different permutation for C · A2 + · a C; · Ai a 426 kinds. A: The days of course there are 426 kinds arranged. 'Example 2 a total of seven people to the A, B. C'D, E, F, G to travel, but not A to A, not B to B, C and not C,[link widoczny dla zalogowanych], small D to go, each to a different place. There are many different travel methods? Solutions of different travel methods A; A + * A + C: · Ai a 2790 kinds. A: There are 2790 kinds of different travel methods. 【Received: 2OO5 291 a lO a

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