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 :
(a) $^{30}C_{7}$
(b) $^{21}C_{8}$
(c) $^{21}C_{7}$
(d) $^{30}C_{8}$

Answer 1

Given : An examiner can assign 30 marks to 8 questions giving not less than 2 marks to any question

To Find :  number of ways

Solution:

Total Marks assigned = 30

8 Questions has to be assigned minimum 2 Marks

hence 8 * 2 = 16 marks

Now we left with 30 - 16 = 14 Marks

2 + 14 = 16  maximum marks can be assigned to a Question

& minimum marks = 2

​  

2 ≤ Q  ≤16

Q1  + Q2 + Q3 + Q4 + Q5 + Q6 + Q7 + Q8 = 30

2 Marks are already assigned to each Question

Hence

q1  + q2 + q3 + q4 + q5 + q6 + q7 + q8 = 30 - 2 * 8

=> q1  + q2 + q3 + q4 + q5 + q6 + q7 + q8 = 14

This the Distribution to be done

Which is Equivalent to

¹⁴⁺⁸⁻¹C₈₋₁

= ²¹C₇

​  

Option C is correct

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