(B) To form numbers using the digits $1, 2, 3, 4$ without repetition,we can form numbers of length $1, 2, 3,$ or $4$.For a number of length $1$,the nu

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$^4P_1 + ^4P_2 + ^4P_3 + ^4P_4$

(B) To form numbers using the digits $1, 2, 3, 4$ without repetition,we can form numbers of length $1, 2, 3,$ or $4$.For a number of length $1$,the number of ways is $^4P_1$.For a number of length $2$,the number of ways is $^4P_2$.For a number of length $3$,the number of ways is $^4P_3$.For a number of length $4$,the number of ways is $^4P_4$.Therefore,the total number of ways is the sum of these possibilities: $^4P_1 + ^4P_2 + ^4P_3 + ^4P_4$.

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

Medium

How many numbers can be formed using the digits $1, 2, 3, 4$ if repetition of digits is not allowed?

A
$^4P_4$
B
$^4P_1 + ^4P_2 + ^4P_3 + ^4P_4$
C
$^4P_1 + ^4P_2 + ^4P_3$
D
$^4P_3$

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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 the letters of the word $RACHIT$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $RACHIT$?

Difficult

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If the number of words,with or without meaning,which can be made using all the letters of the word $MATHEMATICS$ in which $C$ and $S$ do not come together,is $(6 !) k$,then $k$ is equal to $............$.

DifficultJEE MAIN 2023

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How many numbers less than $1000$ can be formed using the digits $0, 1, 2, 4,$ and $5$ if repetition of digits is not allowed?

Medium

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$n$-digit numbers are formed using only three digits $2, 5,$ and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed is:

MediumJEE MAIN 2018

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${ }^{15} P_8 = A + 8 \cdot { }^{14} P_7 \Rightarrow A = $

DifficultAP EAMCET 2011

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How many numbers can be formed using the digits $1, 2, 3, 4$ if repetition of digits is not allowed?

Similar Questions

If the letters of the word $RACHIT$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $RACHIT$?

If the number of words,with or without meaning,which can be made using all the letters of the word $MATHEMATICS$ in which $C$ and $S$ do not come together,is $(6 !) k$,then $k$ is equal to $............$.

How many numbers less than $1000$ can be formed using the digits $0, 1, 2, 4,$ and $5$ if repetition of digits is not allowed?

$n$-digit numbers are formed using only three digits $2, 5,$ and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed is:

${ }^{15} P_8 = A + 8 \cdot { }^{14} P_7 \Rightarrow A = $

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