(A) For the permutation ${}^{n}P_{r}$ to be defined,we must have $n \ge r \ge 0$ and $n, r$ must be non-negative integers.Here,$n = 7-x$ and $r = x-1$

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(A) For the permutation ${}^{n}P_{r}$ to be defined,we must have $n \ge r \ge 0$ and $n, r$ must be non-negative integers.Here,$n = 7-x$ and $r = x-1$.Condition $1$: $n \ge r \implies 7-x \ge x-1 \implies 8 \ge 2x \implies x \le 4$.Condition $2$: $r \ge 0 \implies x-1 \ge 0 \implies x \ge 1$.Condition $3$: $n \ge 0 \implies 7-x \ge 0 \implies x \le 7$.Combining these,we get $1 \le x \le 4$.Since $x$ must be an integer for the permutation notation,the domain is $\{1, 2, 3, 4\}$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

The domain of the function $f(x) = {}^{7-x}P_{x-1}$ is:

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A
$x \in \{1, 2, 3, 4\}$
B
$x \in \{2, 3, 4\}$
C
$x \in \{1, 2, 3, 4, 5\}$
D
$x \in \{1, 2, 3, 4, 5, 6\}$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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