SATHEE: Permutations And Combinations Question 195

Permutations And Combinations Question 195

Question: The number of ordered triplets of positive integers which are solutions of the equation $ x+y+z=100 $ is

Options:

A) 6005

B) 4851

C) 5081

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

The number of triplets of positive integers which are solutions of $ x+y+z=100 $ . $ = $ coefficient of $ x^{100} $ in $ {{(x+x^{2}+x^{3}+…..)}^{3}} $ = coefficient of $ x^{100} $ in $ x^{3}{{(1-x)}^{-3}} $ = coefficient of $ x^{100} $ in $ x^{3}( 1+3x+6x^{2}+….+\frac{(n+1)(n+2)}{2}x^{n}+….. ) $ $ =\frac{(97+1)(97+2)}{2}=49\times 99=4851 $ .

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Permutations And Combinations Question 195

Question: The number of ordered triplets of positive integers which are solutions of the equation $ x+y+z=100 $ is

Options:

Answer:

Solution:

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