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If n=""^(m)C(2) the valuen of ""^(n)C(2)...

If `n=""^(m)C_(2)` the valuen of `""^(n)C_(2)` is given by

A

`""^(m+1)C_(4)`

B

`""^(m-1)C_(4)`

C

`""^(m+2)C_(4)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`n=""^(m)C_(2)=(m(m-1))/(2)`
`:.""^(n)C_(2)=(n(m-1))/(2)`
`implies""^(n)C_(2)=(m(m-1))/(4){(m(m-1))/(2)-1}`
`implies""^(n)C_(2)=(1)/(8)m(m-1)(m^(2)-m-2)`
`implies""^(n)C_(2)=(1)/(8)m(m-1)(m-2)(m+1)`
`implies""^(n)C_(2)=3{(1)/(24)(m+1)m(m-1)(m-2)}=3xx""^(m+3)C_(4)`
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