How many different ways can the letters of the word CONSTITUTION be arranged? How many of these will have the letter N, both at the beginning and at the end?
Answers
Answer:
(a) 554400
(b) 151200
Step-by-step explanation:
Hi,
Given the word CONSTITUTION, which consists of 7 distinct
letters, with N repeating twice, O repeating twice, I repeating
twice and T repeating thrice,
So, the number of distinct ways of arranging the letters of the
word CONSTITUTION are 12!/3!2!2!2! = 554400*
We need to divide by 2! since N is repeating thrice, and all the 2!
permutation between N's will result in the same arrangement
We need to divide by 2! since O is repeating thrice, and all the
2! permutation between O's will result in the same arrangement
We need to divide by 2! since I is repeating thrice, and all the 2!
permutation between I's will result in the same arrangement
We need to divide by 3! since T is repeating thrice, and all the 3!
permutation between T's will result in the same arrangement.
(a) So, different ways of arranging the letters of the word
CONSTITUTION are 554400
Suppose both the N's are t he start and one at the end, then we
need to arrange the remaining 10 letters of which 6 are distinct
and T repeating thrice, I repeating twice and O repeating thrice,
So the number of way of arranging are 10!/3!2!2! = 151200
We need to divide by 2! since O is repeating thrice, and all the
2! permutation between O's will result in the same arrangement
We need to divide by 2! since I is repeating thrice, and all the 2!
permutation between I's will result in the same arrangement
We need to divide by 3! since T is repeating thrice, and all the 3!
permutation between T's will result in the same arrangement.
(b) So, different ways of arranging the letters of the word
CONSTITUTION such that both the n's are at the start and at the
end are 151200
Hope, it helps !
Answer:
here's the right as follows hope it's usefull
