SATHEE: Permutations And Combinations Question 190

Permutations And Combinations Question 190

Question: In how many ways can Rs. 16 be divided into 4 person when none of them get less than Rs. 3

Options:

A) 70

B) 35

C) 64

D) 192

Show Answer

Answer:

Correct Answer: B

Solution:

Required number of ways = Coefficient of $ x^{16} $ in $ {{(x^{3}+x^{4}+x^{5}+….+x^{7})}^{4}} $ = Coefficient of $ x^{16} $ in $ x^{12} $ $ {{(1+x+x^{2}+….x^{4})}^{4}} $ = Coefficient of $ x^{16} $ in $ x^{12}{{(1-x^{5})}^{4}}{{(1-x)}^{-4}} $ = Coefficient of $ x^{4} $ in $ {{(1-x^{5})}^{4}}{{(1-x)}^{-4}} $ = Coefficient of $ x^{4} $ in $ (1-4x^{5}+…) $ $ [ 1+4x+….+\frac{(r+1)(r+2)(r+3)}{3!}x^{r} ] $ = $ \frac{(4+1)(4+2)(4+3)}{3!}=35 $ . Aliter: Remaining 4 rupees can be distributed in $ ^{4+4-1}{C _{4-1}} $ i.e., 35 ways.

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Permutations And Combinations Question 190

Question: In how many ways can Rs. 16 be divided into 4 person when none of them get less than Rs. 3

Options:

Answer:

Solution:

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