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

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

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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The ST 455 6% 5% form is used by businesses in South Carolina to report sales and use tax. This form is essential for compliance with The South Carolina Department Of Revenue requirements. By accurately completing the ST 455 6% 5%, businesses can ensure they are meeting their tax obligations.

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