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# In how many different ways can the 24 members of a sorority

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Intern
Joined: 12 Dec 2004
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In how many different ways can the 24 members of a sorority [#permalink]  05 Jan 2005, 20:04
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In how many different ways can the 24 members of a sorority elect a president, a VP, and a sec, assuming that no member can hold more than one office? In what % of these possibilities will Mary Jones, one of the 24 members of this sorority, be elected to one of the 3 offices?
VP
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a) 24X23X22 = 24P3

b) For Pres or VP or sec: 3(1x23x22) So % = 3x23x22 / 24x23x22 = 1/8 = 12.5 %
VP
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[quote="vprabhala"][quote="banerjeea_98"]a) 24X23X22 = 24P3

b) For Pres or VP or sec: 3(1x23x22) So % = 3x23x22 / 24x23x22 = 1/8 = 12.5 %[/quote]
can you explain B further..[/quote]

B) In B there can be 3 scenarios. Mary can be chosen for VP, Pres or Sec. In every scenario, there is only 1 way to choose Mary and 23 and 22 ways to choose other posts. As there are 3 such scenarios, you have to add number of ways for all scenarios i.e. 1x23x22 + 1x23x22 + 1x23x22. Hope this makes it clear.
Intern
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Quote:
a) 24X23X22 = 24P3

b) For Pres or VP or sec: 3(1x23x22) So % = 3x23x22 / 24x23x22 = 1/8 = 12.5 %

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