Home
Class 12
MATHS
Consider all possible permutations of th...

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

Text Solution

Verified by Experts

The correct Answer is:
`(A to p; B to s; C to q; D to q)`
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 xx 5!`
C. If D, L, N are not in last five positions
`larr D, L, N, N rarr larrE, E, E, A, O rarr`
Total number of permutations `= (4!)/(2!) xx (5!)/(3!) = 2 xx 5!`
D. Total number of odd positions = 5
Permutations of AEEEO are `(5!)/(3!)`.
Total number of even positions = 4
`therefore` Number of permutations of `N, N, D, L = (4!)/(2!)`
`rArr` Total number of permutations `= (5!)/(3!) xx (4!)/(2!) = 2 xx 5!`
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of permutations of the letter of the word 'CONSEQUENCE' is

Find the number of permutations of the letters of the word ALLAHABAD.

The number of permutations of the letters of the word BANANA is ………………..

The number of permutations of the letters of the word 'CONSEQUENCE' in which all the three Es are together is

Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time ?

The number of permutation of all the letters of the word PERMUTATION such that any two consecutive letters in the arrangement are neither both vowels nor both identical is

If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E ?

Given are six 0' s, five 1' s and four 2's . Consider all possible permutations of all these numbers. [A permutations can have its leading digit 0 ]. How many permutations have the first 0 preceding the first 1 ?

Given are six 0' s, five 1' s and four 2's . Consider all possible permutations of all these numbers. [A permutations can have its leading digit 0 ]. In how many permutations does the first 0 precede the first 1 and the first 1 precede first 2 .