The number of ways of choosing triplet `(x , y ,z)`such that `zgeqmax{x, y}a n dx ,y ,z in {1,2, n ,n+1}`isa. `^n+1C_3+^(n+2)C_3`b. `n(n+1)(2n+1)//6`c. `1^2+2^2++n^2`d. `2((^(n+2)C_3))_(-^(n+2))C_2`A. `.^(n+1)C_(3)+.^(n+2)C_(3)`B. `(n(n+1)(2n+1))/(6)`C. `1^(2)+2^(2)+3^(2)+ . . .+n^(2)`D. `2(.^(n+2)C_(3))-.^(n+1)C_(2)`

The number of ways of choosing triplet `(x , y ,z)`such that `zgeqmax{

1.	The number of ways of choosing triplet `(x , y ,z)`such that `zgeqmax{x, y}a n dx ,y ,z in {1,2, n ,n+1}`isa. `^n+1C_3+^(n+2)C_3`b. `n(n+1)(2n+1)//6`c. `1^2+2^2++n^2`d. `2((^(n+2)C_3))_(-^(n+2))C_2`A. `.^(n+1)C_(3)+.^(n+2)C_(3)`B. `(n(n+1)(2n+1))/(6)`C. `1^(2)+2^(2)+3^(2)+ . . .+n^(2)`D. `2(.^(n+2)C_(3))-.^(n+1)C_(2)`
Answer» Correct Answer - A::B::C::D Triplets with (i) x=y`ltz` (ii) `x lt y lt z` (iii) `y lt x lt z` can be chosen in `.^(n+1)C_(2),.^(n+1)C_(3),.^(n+1)C_(3)` ways. `therefore.^(n+1)C_(2)+.^(n+1)C_(3)+.^(n+1)C_(3)=.^(n+2)C_(3)+.^(n+1)C_(3)` `=2(.^(n+2)C_(3))-.^(n+1)C_(2)` `=(n(n-1)(2n+1))/(6)`

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