(D) The total number of ways to place $3$ distinct letters into $3$ distinct envelopes is $3! = 3 \times 2 \times 1 = 6$.Out of these $6$ possible arr

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(D) The total number of ways to place $3$ distinct letters into $3$ distinct envelopes is $3! = 3 \times 2 \times 1 = 6$.Out of these $6$ possible arrangements,only $1$ arrangement corresponds to all letters being placed in their correct envelopes.Therefore,the required probability is $\frac{1}{3!} = \frac{1}{6}$.

Class 11 Mathematics Permutations and Combinations Division into groups, Derangements

Easy

Three letters are to be sent to different persons,and addresses on the three envelopes are also written. Without looking at the addresses,the probability that all the letters go into the right envelopes is equal to

A
$\frac{1}{27}$
B
$\frac{1}{9}$
C
$\frac{4}{27}$
D
$\frac{1}{6}$

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Class 11

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Chapter

Permutations and Combinations

Subtopic

Division into groups, Derangements

If there are $6$ letters and $6$ corresponding envelopes,in how many ways can all the letters be placed in the wrong envelopes?

Medium

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In an examination,$5$ students have been allotted their seats as per their roll numbers. The number of ways,in which none of the students sits on the allotted seat,is $..........$.

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There are $4$ envelopes with addresses and $4$ corresponding letters. The probability that no letter goes into its correct envelope is:

Medium

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There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is

Difficult

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There are $4$ balls of different colors and $4$ boxes of the same colors as the balls. In how many ways can $2$ balls be placed in the boxes such that they do not match their respective colors?

Difficult

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Three letters are to be sent to different persons,and addresses on the three envelopes are also written. Without looking at the addresses,the probability that all the letters go into the right envelopes is equal to

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If there are $6$ letters and $6$ corresponding envelopes,in how many ways can all the letters be placed in the wrong envelopes?

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