P&C#0

Number Theory Level 3

Pls type the correct option number as the answer


The answer is 4.

Aakhyat Singh by Aakhyat Singh , 20, India

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2 solutions

Aakhyat Singh
Feb 20, 2018

The no. of ways in which 12 balls can be selected would be = to the no. of solns. for the equation a+b+c+d=12 (0<=a,b,c,d<=12) which is(coefficient of x^12 in the equation (1+x+x^2+....+x^12)^4 =(12+4-1)!/((12)!*(3)!)=455 Credit- @Aaghaz Mahajan

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∗ ∗ A S m a l l D o u b t ∗ ∗ **A Small Doubt**

Wouldnt the no. of ways to select the balls essentially mean the manner in which they are taken.....

For ex. lets the colours be B,R,G,Y

one way it could be selected............................................ BRBGRYGBRGRY

another way...................................................................... RGRGYBGYRBGY

YET ANOTHER................................................................ GGGYRGYGBBYG

Wouldnt this lead to the answer as 4 12 4^{12}

I dont know if I interpreted it wrong........ anyhow can u tell me why i am wrong here.

Kartik Jay - 3 years, 3 months ago

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No , bcoz we have to just select the balls irrespective of the way @Kartik Jay .

Aakhyat Singh - 3 years, 3 months ago

question must mention of selecting all 12 balls at once.if it was selecting one by one then your answer is perfectly fine

Onkar Sapkal - 1 year, 3 months ago
Aaghaz Mahajan
Feb 19, 2018

Simply use the Starts and Bars technique....

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