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If a,b,c and d are odd natural numbers s...

If a,b,c and d are odd natural numbers such that a+b+c+d=20, the number of values of the ordered quadruplet (a,b,c,d) is

A

165

B

455

C

310

D

None of these

Text Solution

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The correct Answer is:
A
Let `a=2x-1,b=2y-1,c=2z-1,d=2w-1`
where, x,y,z,w`inN`
then, `a+b+c+d=20`
`implies x+y+z+w=12`
`therefore`Number of ordered quadruplet`=.^(12-1)C_(4-1)`
`=.^(11)C_(3)=(11*10*9)/(1*2*3)=165`
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