Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For a finite set $A$ , let $∣ A ∣$ denote the number of elements in the set $A$ . Also, let $F$ denote the set of all functions $f : {1, 2, \dots, n} \to {1, 2, \dots, k}$ where $n \geq 3$ and $k \geq 2$ , satisfying $f (i) \neq = f (i + 1)$ for every $i$ , $1 \leq j \leq n - 1$

$∣ F ∣ =$

Options:

Answer:

Solution:

The image of element 1 can be chosen in $k$ ways. For each of the remaining $(n - 1)$ elements, the image can be defined in $(k - 1)$ ways, since $f (i) \neq = f (i + 1)$ . Therefore, the total number of mappings is $F = k (k - 1)^{n - 1}$

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

⏱ 2mℹ️ Source: QB

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