(B) Given that $a = {}^{x+2}P_{x+2} = (x+2)!$ $b = {}^{x}P_{11} = \frac{x!}{(x-11)!}$ $c = {}^{x-11}P_{x-11} = (x-11)!$ Given the equation $a = 182bc$

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(B) Given that $a = {}^{x+2}P_{x+2} = (x+2)!$ $b = {}^{x}P_{11} = \frac{x!}{(x-11)!}$ $c = {}^{x-11}P_{x-11} = (x-11)!$ Given the equation $a = 182bc$: $(x+2)! = 182 \times \frac{x!}{(x-11)!} \times (x-11)!$ $(x+2)(x+1)x! = 182 \times x!$ $(x+2)(x+1) = 182$ Since $182 = 14 \times 13$,we have $(x+2)(x+1) = 14 \times 13$. Comparing the factors,$x+2 = 14$ or $x+1 = 13$. Therefore,$x = 12$.

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

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If $a$ denotes the number of permutations of $(x + 2)$ items taken all at a time,$b$ denotes the number of permutations of $x$ items taken $11$ at a time,and $c$ denotes the number of permutations of $(x - 11)$ items taken all at a time. If $a = 182bc$,find the value of $x$.

A
$15$
B
$12$
C
$10$
D
$18$

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Class 11 Questions

Class 11

Mathematics Questions

Chapter

Permutation and Combination

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

If $7 \cdot ^nP_3 = 20 \cdot ^{n+1}P_2$,then $n = \dots$

Easy

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The number of different nine-digit numbers that can be formed by rearranging the digits of the number $223355888$ such that the odd digits occupy even positions is:

EasyMHT CET 2024

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What is the total number of permutations of the letters of the word $BANANA$?

Medium

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All the letters of the word $GTWENTY$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $GTWENTY$ is:

DifficultJEE MAIN 2024

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If the digits are not allowed to repeat in any number formed by using the digits $0, 2, 4, 6, 8$,then the number of all numbers greater than $10,000$ is equal to $....$

EasyJEE MAIN 2021

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If $a$ denotes the number of permutations of $(x + 2)$ items taken all at a time,$b$ denotes the number of permutations of $x$ items taken $11$ at a time,and $c$ denotes the number of permutations of $(x - 11)$ items taken all at a time. If $a = 182bc$,find the value of $x$.

Similar Questions

If $7 \cdot ^nP_3 = 20 \cdot ^{n+1}P_2$,then $n = \dots$

The number of different nine-digit numbers that can be formed by rearranging the digits of the number $223355888$ such that the odd digits occupy even positions is:

What is the total number of permutations of the letters of the word $BANANA$?

All the letters of the word $GTWENTY$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $GTWENTY$ is:

If the digits are not allowed to repeat in any number formed by using the digits $0, 2, 4, 6, 8$,then the number of all numbers greater than $10,000$ is equal to $....$

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