A committee of 5 is to formed out of 6 gents and 4 ladies. In how many ways can this be done when each committee may have at the most two ladies?

At most 2 ladies means either no lady, 1 lady or 2 lady.Case 1: 0 lady, 5 members from 6 gents can be selected in 6C5 = 6 ways.Case 2: 1 lady, 1 lady can be selected from 4 ladies in 4 ways. Corresponding to each lady selected, rest 4 members can be selected from 6 gents in 6C4 = 12 ways. So, total ways in Case 2 is 48.Case 3: 2 lady, 2 lady can be selected from 4 ladies in 4C2 = 6 ways. Corresponding to two ladies selected, rest 3 members can be selected from 6 gents in 6C3 = 20 ways. So, total ways in Case 3 is 120.Now each case is independent. So, total number of ways is 120 + 48 + 6 = 174.Answer : 174

How do I solve this question? A committee of 5 men and 3 women is to be formed out of 7 men and 6 women. If two particular women are not to be together in the committee, what is the number of committees formed?

Total Available Persons = 7 Men and 6 WomenA committee of 5 Men and 3 Women is to be formed.So, I need to select 5 men out of 7 and it can be done in [math]^7c_5[/math] ways3 women out of 6 can be selected in [math]^6c_3 [/math]waysNow, without any constraints, the number of ways the committee can be selected is:[math]^7c_5 times ^6c_3 = 21 times 20 = 420[/math] waysBut, the question says two particular women should not be there in the committee together. So, to find that, we need to look at the question in another way.Number of ways in which two particular women aren't there together in the committee is same as total number of ways minus the number of ways those two women are definitely there together.Number of ways in which the two women are definitely there can be calculated as:[math]^7c_5 times ^4c_1 = 21 times 4 = 84[/math]Note: As the two women are definitely there, so I just need to select one more woman from the remaining 4.Thus, number of ways to select such that two particular women are never there together is [math](420 - 84) = fbox {336 (Answer)}[/math]

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ST 455 6% 5% the South Carolina Department of Revenue Sctax 2010

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How to pay taxes on your small business small businesses may have to pay a variety of federal and state or local taxes avoid harsh penalties by learning how to pay them you will need estimated tax payments an income tax return excise tax payments employment tax payments sales tax payments and state and local tax payments optional self-employment tax payments step one make quarterly estimated tax payments to the IRS if your total tax bill in a given year will exceed $500 estimated tax payments are due four times a year on April 15 June 15 September 15th and January 15 pay self-employment tax if your annual net earnings will be 400 dollars or more step 2 file an annual income tax return the form you use will depend on how your business is organized whether it is a sole proprietorship partnership corporation or limited liability corporation keep tax related documents for a minimum of 7 years step 3 pay excise tax if your business engages in qualified activities for example excise taxes ar

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