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Question

# n similsr balls each of weight w when weighed in pairs, the sim of the weights of all the possible pairs is 120 is 120 and when they are weighed in triplets, the sum of the weights comes out to be 480 for all possible triplets. Then n is equal to

A
5
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B
10
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C
15
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D
20
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Solution

## The correct option is B 10Given,n = similar balls, each of weight Wwhen,Weight in pair = 120Weight in triplets = 180Now,Total number of selection in pairs=n(n−1)2A/Q120=n(n−1)2⋅2w - (i)Total number of selection in triplets=n(n−1)(n−2)6480=n(n−1)(n−2)6−3w - (ii) Dividing equation (i) and (ii)We get,4480120=3(n−1)(n−2)⋅3w6n(n−1)2⋅2w4=n−2n8+2=n (n = 10 option B)

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