The number of ways of choosing triplet (x,y,z) such that z>max{x,y} and x,y,z∈{1,2,……….n,n+1} is (A) .n+1C3+n+2C3 (B)n(n+1)(2n+1)/6 (C)12+22+…………..+n2 (D) 2(.n+2C3)−(.n+1C2)

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The number of ways of choosing triplet {({x},{y},{z})} such th

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The number of ways of choosing triplet $(x, y, z)$ such that $z > max {x, y}$ and $x, y, z \in {1, 2, \dots\dots\dots . n, n + 1}$ is $(A)$ $.^{n} + 1 C_{3} +^{n + 2} C_{3}$ $(B)$ $n (n + 1) (2 n + 1) / 6$ $(C)$ $1^{2} + 2^{2} + \dots\dots\dots\dots .. + n^{2}$ $(D)$ $2 (.^{n + 2} C_{3}) - (.^{n + 1} C_{2})$

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The number of ways of choosing triplet

(x, y, z)

such that

z > max {x, y}

and

x, y, z \in {1, 2, \dots\dots\dots . n, n + 1}

(A)

.^{n} + 1 C_{3} +^{n + 2} C_{3}

(B)

n (n + 1) (2 n + 1) / 6

(C)

1^{2} + 2^{2} + \dots\dots\dots\dots .. + n^{2}

(D)

2 (.^{n + 2} C_{3}) - (.^{n + 1} C_{2})

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Question Text

The number of ways of choosing triplet

(x, y, z)

such that

z > max {x, y}

and

x, y, z \in {1, 2, \dots\dots\dots . n, n + 1}

(A)

.^{n} + 1 C_{3} +^{n + 2} C_{3}

(B)

n (n + 1) (2 n + 1) / 6

(C)

1^{2} + 2^{2} + \dots\dots\dots\dots .. + n^{2}

(D)

2 (.^{n + 2} C_{3}) - (.^{n + 1} C_{2})