Consider all possible permutations of the letters of the word $ENDEANOEL$. Match the Statements / Expressions in $Column I$ with the Statements / Expressions in $Column II$.
$Column I$$Column II$
$(A)$ The number of permutations containing the word $ENDEA$ is$(p)$ $5!$
$(B)$ The number of permutations in which the letter $E$ occurs in the first and the last positions is$(q)$ $2 \times 5!$
$(C)$ The number of permutations in which none of the letters $D, L, N$ occurs in the last five positions is$(r)$ $7 \times 5!$
$(D)$ The number of permutations in which the letters $A, E, O$ occur only in odd positions is$(s)$ $21 \times 5!$

  • A
    $(A) \rightarrow (s); (B) \rightarrow (r); (C) \rightarrow (p); (D) \rightarrow (q)$
  • B
    $(A) \rightarrow (s); (B) \rightarrow (r); (C) \rightarrow (p); (D) \rightarrow (q)$
  • C
    $(A) \rightarrow (p); (B) \rightarrow (s); (C) \rightarrow (q); (D) \rightarrow (q)$
  • D
    $(A) \rightarrow (r); (B) \rightarrow (q); (C) \rightarrow (q); (D) \rightarrow (p)$

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Similar Questions

In a high school,a committee has to be formed from a group of $6$ boys $M_1, M_2, M_3, M_4, M_5, M_6$ and $5$ girls $G_1, G_2, G_3, G_4, G_5$.
$(i)$ Let $\alpha_1$ be the total number of ways in which the committee can be formed such that the committee has $5$ members,having exactly $3$ boys and $2$ girls.
$(ii)$ Let $\alpha_2$ be the total number of ways in which the committee can be formed such that the committee has at least $2$ members,and having an equal number of boys and girls.
$(iii)$ Let $\alpha_3$ be the total number of ways in which the committee can be formed such that the committee has $5$ members,at least $2$ of them being girls.
$(iv)$ Let $\alpha_4$ be the total number of ways in which the committee can be formed such that the committee has $4$ members,having at least $2$ girls and such that both $M_1$ and $G_1$ are $NOT$ in the committee together.
$LIST-I$$LIST-II$
$P$. The value of $\alpha_1$ is$1. 136$
$Q$. The value of $\alpha_2$ is$2. 189$
$R$. The value of $\alpha_3$ is$3. 192$
$S$. The value of $\alpha_4$ is$4. 200$
$5. 381$
$6. 461$

The correct option is:

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The letters of the word $ASSASSIN$ are written down at random in a row. The probability that no two $S$ occur together is

The number of ways in which four letters of the word '$MATHEMATICS$' can be arranged is given by

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The difference between an integer $n$ and its cube $n^3$ is always divisible by which of the following?

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