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The number of ways in which 16 sovereigns can be distributed among 3 applicants such that each applicant does not receive less than 3 sovereigns is:
Correct answer is '36'. Can you explain this answer?
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The number of ways in which 16 sovereigns can be distributed among 3 ...
Let x, y, z be the number of sovereigns received by the 3 applicants.
Then x ≥ 3, y ≥ 3, z ≥ 3 and x + y + z = 16.
Let u = x - 3, v = y - 3 and w = z - 3,then u ≥ 0, v ≥ 0, w ≥ 0
So, u + 3 + v + 3 + w + 3 = 16
Or, u + v + w = 7
The total number of the solutions of the given equation is 7+3-1C3-1 = 9C2 = 36.
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The number of ways in which 16 sovereigns can be distributed among 3 applicants such that each applicant does not receive less than 3 sovereigns is:Correct answer is '36'. Can you explain this answer?
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