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If m=nC2, show that, mC2=3.(n+1)C4...

If `m=nC_2`, show that, `mC_2=3.(n+1)C_4`

Text Solution

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Here, `m = n_(C_2)`
`=> m = (n!)/((2!)(n-2))! = (n(n-1))/2`
Now, `m_(C_2) = (m(m-1))/2`
Putting value of `m`,
`m_(C_2) = (((n(n-1))/2)((n(n-1))/2)-1)/2`
`=(n(n-1))/4[(n^2-n-2)/2]`
`=(n(n-1)(n+1)(n-2))/8`
`=(3n(n-1)(n+1)(n-2))/24`
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