(B) Each of the $n$ distinct objects can be placed in either of the $2$ different boxes. Since each object has $2$ choices,the total number of ways to

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(B) Each of the $n$ distinct objects can be placed in either of the $2$ different boxes. Since each object has $2$ choices,the total number of ways to distribute $n$ distinct objects into $2$ different boxes is $2 \times 2 \times 2 \times \dots \times 2$ ($n$ times). Therefore,the total number of ways is $2^n$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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The number of ways in which $n$ distinct objects can be put into two different boxes is

AP EAMCET 2021 All AP EAMCET

A
${ }^n P_2$
B
$2^n$
C
${ }^n C_2$
D
$n(n-1)(n-2)$

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Class 11

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Chapter

Permutations and Combinations

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

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The number of natural numbers less than $1000$,in which no two digits are repeated,is:

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How many $6$-digit numbers can be formed using the digits of the number $112233$?

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There are $10$ lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is

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Ten persons,amongst whom are $A, B$ and $C$,are to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is:

Medium

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$4$ buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by a different bus,then the total number of possible ways is:

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The number of ways in which $n$ distinct objects can be put into two different boxes is

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The number of natural numbers less than $1000$,in which no two digits are repeated,is:

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