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sir, pl. help me to solve following problems of permutation & combination- Q1. how many divisors of 9000 are even but not divisible by 4?also find the sum of such nos. Q2. the no. of ways an examiner can assign 30 marks to 8 ques., awarding not less than 2 marks to any ques. is

sir,
pl. help me to solve following problems of permutation & combination-


Q1. how many divisors of 9000 are even but not divisible by 4?also find the sum of such nos.



Q2. the no. of ways an examiner can assign 30 marks to 8 ques., awarding not less than 2 marks to any ques. is

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1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
9 years ago
Ans 1

9000= 23x32x53 . . . . (1)

Total number of divisors = (3+1)(2+1)(3+1)= 48

It is required to find even factors for which 2 has to be included and higher power of 2 cannot be taken into divisors as then it will become divisible by 4

So divisor should look like 2x3px5q
where p can take values 0,1,2 and q can be 0,1,2,3 ( From (1) )

Total such divisors will be 3x4=12.

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