Combinations
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The document discusses combinations and provides examples to illustrate the concept. Combinations refer to arrangements of objects where order does not matter. The document defines the "Choose" formula used to calculate combinations as nCr = n! / (n-r)!r!. Several examples are provided applying the formula to problems involving choosing lottery numbers, arranging books on a shelf, and making necklaces from beads.
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This document appears to be notes from a math lesson covering topics like factorials, permutations, combinations, and logarithms. It provides examples of calculations and explains concepts like:
- 5! = 120, showing the factorial of 5 is equal to 120
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The document discusses circular permutations, which refers to the number of arrangements that can be made of n objects arranged in a circle. It gives the formula for calculating circular permutations as (n-1)!. It provides examples of using this formula to calculate the number of ways to seat people or arrange beads in a circular configuration. It also discusses a special case where the objects can be flipped over, in which case the formula is (n-1)!/2. Finally, it asks how many ways 4 married couples can be seated at a circular table if spouses sit opposite each other or if men and women alternate.
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The document discusses circular permutations, which refers to the number of arrangements that can be made of n objects arranged in a circle. It provides the formula for calculating circular permutations as (n-1)!. It also discusses using the formula to calculate the number of ways to seat people or arrange beads around a circular table or bracelet. Some examples are worked out, such as seating 3 people which has 2 arrangements, or seating 4 people which has 6 arrangements. It also discusses applying the formula to problems involving seating married couples around a table, calculating the number of arrangements if spouses sit opposite each other as 6 or if men and women alternate as 144.
Circular Permutation
The document introduces circular permutation as the number of ordered arrangements that can be made of n objects in a circle. It is calculated as (n-1)!. Several examples are provided to illustrate circular permutation for seating people around a table and arranging beads on a bracelet. The document also considers the number of ways 4 married couples can be seated if spouses sit opposite each other [(n-1)!/3!] or if men and women alternate [3! x 4! = 144].
Circular Permutation
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3:国家专业人才认证中心颁发入库证书
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1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
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本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
Divertidamente SLIDE muito lindo e criativo, pptx
Slide criativo e muito lindo, apenas editar, muito simples
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Combinations
- 2. Hello there! I'm Mary Ann, and I will be your scribe for today. We started off with a few circle permutation questions as a warmup. It was quite simple in the beginning, but, little did we know what Mr. K had in store for our class today. It was called COMBINATIONS. Defenition: An arrangement of objects where order does not matter. (The opposite of a permutation; where order does matter.)
- 3. n! This is known as the quot;Choosequot; = nCr Formula: formula. (n r)!r! n is the number of objects to choose from. r is the number of objects to be arranged. Example: You have 49 numbers in the 6/49 lottery to choose from and want to choose 6 numbers for your ticket. you will then have.. 49! 49! 49C6 = = 13 983 816 = (49 6)!6! (43)!6! ways to make your ticket.
- 4. Example: In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together? These three books have to be together at all times. But within these three books, they can also be arranged in 3! ways. The same goes with the six books; 6! ways. (3!)(6!) (6)(720) 4320 ways to arrange the books.
- 5. Example: How many differnt necklaces of 12 beads can each be made from 18 beads of different colours? In this question, you are to choose 12 beads from 18 beads. ∴ 18C12 Step 2: Step 1: 18! This side takes care The (12 1)! of the circular quot;Choosequot; (1812)!12! 2 permutation idea, Formula 18! 11! since the necklace (6)!12! 2 is a circle and can be flipped over. 18 564 19 958 400 (18 564)(19 958 400)
- 6. In the afternoon class, while Mr. K had to run out for a short while, we had a quiz. (Refer to the post below to look at the slides where members of our class wrote down the solutions). The solutions are pretty straight forward, so I don't think I have to make any clarifications on it. If their are any questions though, please comment on this post and I, or someone else who can explain it, will be glad to help. :) The next scribe is !! Ecko Montana !!