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31 May 2020, 02:53
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
50% (01:46) correct
50%
(01:33)
wrong
based on 167
sessions
History
Date
Time
Result
Not Attempted Yet
The number of positive integral solutions of the equation a+b+c+d+e = 30 is?
A.25173
B.23517
C.25731
D.23751
E.23518
A.25173
B.23517
C.25731
D.23751
E.23518
31 May 2020, 06:09
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MBADream786
RULE:
For any equation a+b+c+d = n
where n = Total Balls to be distributed and r = 4 (Number of variables)
The number of Positive solutions \(= (n-1)C_{r-1}\)
i.e. Positive Integer solution of the equation a+b+c+d+e = 30 will be \((30-1)C_{5-1} = 23751\)
Answer: Option D
DERIVATION OF PARTITION RULE:
General Discussion
31 May 2020, 03:59
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MBADream786
So 30 has to be distributed amongst 5 sets a,b,c,d and e. As we are looking at positive integral solution, let us give 1 each to all 5.
Remaining now =30-5=25
So let us now add 4 partItions so that we can distribute these in 5 sets and then choose these 4 partitions
=> (25+4)C4=29*28*27*26/4!=29*7*9*13=23751
D
