Advertisements
Advertisements
Question
Find the number of arrangements of letters in the word CONSTITUTION that begin and end with N.
Solution
There are 12 letters in the word CONSTITUTION, in which ‘O’, ‘N’, ‘I’ repeat two times each, ‘T’ repeats 3 times.
The arrangement starts and ends with ‘N’, 10 letters other than N can be arranged between two N, in which ‘O’ and ‘I’ repeat twice each and ‘T’ repeats 3 times.
∴ Total number of arrangements with the letter N at the beginning and at the end = `(10!)/(2!2!3!)`
APPEARS IN
RELATED QUESTIONS
Find the number of permutations of letters of the following word: DIVYA
You have 2 identical books on English, 3 identical books in Hindi, and 4 identical books on Mathematics. Find the number of distinct ways of arranging them on a shelf.
A coin is tossed 8 times. In how many ways can we obtain 4 heads and 4 tails?
A bag has 5 red, 4 blue, and 4 green marbles. If all are drawn one by one and their colours are recorded, how many different arrangements can be found?
Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have letters M and T never together?
Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have all vowels together?
How many different words are formed if the letter R is used thrice and letters S and T are used twice each?
Find the number of arrangements of letters in the word MUMBAI so that the letter B is always next to A.
Find the number of different ways of arranging letters in the word ARRANGE. How many of these arrangements the two R’s and two A’s are not together?
How many different 6-digit numbers can be formed using digits in the number 659942? How many of them are divisible by 2?
Find the number of different ways of arranging letters in the word PLATOON if consonants and vowels occupy alternate positions.
