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permutation and combination
Tendua
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Combinatory
Nov 26, 2015
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Jun 27, 2017
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Arjun
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in how many ways 10 identical blue marbles and 5 identical green marbles be arranged in a row so that no two green marbles are together??
combinatory
Tendua
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Nov 26, 2015
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First we place the 10 blue balls in 1 way because they are all identical :
__B1__ B2__B3__B4__B5__B6__B7__B8__B9__B10__
Since no 2 green balls are together only place we have is to place the green balls in between blue balls . There are 11 available places to place the green balls : Therefore we can select any 5 places as 11C5 . Then we arrange the 5 balls in 1 way because they are identical .
Therefore the answer is 11C5 = 462.
Riya Roy(Arayana)
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Nov 26, 2015
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Tendua
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Tendua
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Nov 26, 2015
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what if they are not identical . then what will be the case
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Riya Roy(Arayana)
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If they are not identical you do multiply 11C5 with 10! and 5! becoz blue balls can arrange among themselves in 10! ways and 5 green balls in 5! different ways .
Therefore : 11C5*10!*5! would have been the answer .
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prathams
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Nov 26, 2015
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We have already place 5 green balls in 11C5 ways, then why we again multiplying 5! ?
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Gate Mm
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Dec 9, 2015
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Why isnt it 11P5 coz we are arranging the 5 green balls in restricted places of 11 poistions.And the blue balls are suposed to arrange in 10! ways.now since they are identical it is 10!/10!.Plz clarify someone,.
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