(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

How many $5$-digit numbers can be formed using the digits $0, 1, 2, 3, 5, 7$ without repetition? If all such numbers are arranged in ascending order,what is the rank of the number $70513$?

MediumAP EAMCET 2025

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Evaluate $\frac{n!}{(n-r)!}$,when $n=9, r=5$.

Easy

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DifficultJEE MAIN 2023

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Easy

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Given $4$ flags of different colours,how many different signals can be generated,if a signal requires the use of $2$ flags one below the other?

Easy

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

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How many $5$-digit numbers can be formed using the digits $0, 1, 2, 3, 5, 7$ without repetition? If all such numbers are arranged in ascending order,what is the rank of the number $70513$?

Evaluate $\frac{n!}{(n-r)!}$,when $n=9, r=5$.

The number of seven-digit odd numbers that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is $.......$

How many numbers lying between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$ if each digit is used only once in each number?

Given $4$ flags of different colours,how many different signals can be generated,if a signal requires the use of $2$ flags one below the other?

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