Permutations and Combinations 1 Question 12

12. Consider all possible permutations of the letters of the word ENDEANOEL.

(2008,6M)

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. 2×5!
C. The number of permutations in which none of the
letters D, L, N occurs in the last five positions, is
r. 7×5!
D. The number of permutations in which the letters A, E,
O occur only in odd positions, is
s. 21×5!
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Answer:

Correct Answer: 12. ((Ap;Bs;Cq;Dq))

Solution:

  1. A. If ENDEA is fixed word, then assume this as a single letter. Total number of letters =5

Total number of arrangements =5 !.

B. If E is at first and last places, then total number of permutations =7!/2!=21×5 !

C. If D,L,N are not in last five positions

D,L,N,N→←E,E,E,A,O

Total number of permutations =4!2!×5!3!=2×5 !

D. Total number of odd positions =5

Permutations of AEEEO are 5!3!.

Total number of even positions =4

Number of permutations of N, N, D, L =4!2!

Total number of permutations =5!3!×4!2!=2×5 !



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