34. Consider all possible permutations of the letters of the...

34. 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 and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the ORS. 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 (q) $2 \times 5 !$ the first and the last positions is (C) The number of permutations in which none of the letters (r) $7 \times 5 !$ D, L, N occurs in the last five positions is (D) The number of permutations in which the letters A, E, O (s) $21 \times 5 !$ occur only in odd positions is

34. 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 and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the ORS.
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
(q) $2 \times 5 !$
the first and the last positions is
(C) The number of permutations in which none of the letters
(r) $7 \times 5 !$
D, L, N occurs in the last five positions is
(D) The number of permutations in which the letters A, E, O
(s) $21 \times 5 !$
occur only in odd positions is

Key Concepts

Restricted Arrangements with Parity Constraints

This concept involves restrictions based on the parity (odd or even nature) of the positions available in the arrangement. When certain objects must occupy only odd or only even positions, the positions available for those objects are limited, which changes the method for counting the valid arrangements.

Exclusion of Specific Elements from Certain Positions

This approach is applied when particular objects are not allowed to appear in designated positions within an arrangement. It often requires counting only the arrangements that meet the exclusion criteria or using methods like complementary counting to subtract the unwanted cases.

Permutations with Repeated Elements

This concept involves counting the number of distinct arrangements of objects where some objects are identical. In such cases, instead of simply taking the factorial of the total number of objects, the total is divided by the factorial of the number of repetitions for each set of identical objects to eliminate overcounting.

Block Method in Permutations

This technique is used when a group of objects or letters must appear consecutively in a specified order. The group is treated as a single entity during the arrangement process, and then the internal ordering of the block is accounted for if necessary.

Positional Restrictions in Arrangements

This concept deals with constraints where specific objects are required to occupy fixed positions in an arrangement. By assigning these fixed positions first, the remaining objects are arranged in the leftover positions, thereby altering the total count of valid arrangements.

Transcript

Please give Ace some feedback