Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediumsingle choice

Let A be a set of $n (\geq 3)$ distinct elements. The number of triplets $(x, y, z)$ of the elements of A in which at least two coordinates are equal is

Options:

Answer:

Solution:

Total no. of triplets without restriction $= n^{3}$ . No. of triplets with different coordinates $= n P_{3}$ .

Required ways:

$= n^{3} - n P_{3} = n^{3} - n (n - 1) (n - 2) = n^{3} - (n^{3} - 3 n^{2} + 2 n) = n^{3} - n^{3} + 3 n^{2} - 2 n = 3 n^{2} - 2 n$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

⏱ 2mℹ️ Source: QB

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