SATHEE: Permutations And Combinations Question 378

Permutations And Combinations Question 378

Question: The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is:

Options:

A) $ ^{30}C_7 $

B) $ ^{21}C_8 $

C) $ ^{21}C_7 $

D) $ ^{30}C_8 $

Show Answer

Answer:

Correct Answer: C

Solution:

[c] 30 marks to be allotted to 8 questions. Each questions has to be given $ \ge 2marks $ Let questions be a, b, c, d, e, f, g, h and $ a+b+c+d+e+f+g+h=30 $ Let $ a=a_1+2 $ so, $ a_1\ge 0, $ $ b=a_2+2so,a_2\ge 0,….a_8\ge 0 $ So, $ . \begin{matrix} a_1+a_2+…+a_8 \\ +2+2+….+2 \\ \end{matrix} }=30 $

$ \Rightarrow a_1+a_2+…+a_8=30-16=14 $ So, this is a problem of distributing 14 articles in 8 groups. Number of ways $ {{=}^{14+8-1}}{C _{8-1}}{{=}^{21}}C_7 $

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Permutations And Combinations Question 378

Question: The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is:

Options:

Answer:

Solution:

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