If the different permutations of the word EXA | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The word $EXAMINATION$ consists of $11$ letters: $A, A, E, I, I, M, N, N, O, T, X$.To find the number of words before the first word starting with

Vedclass · Accepted Answer

$907200$

Vedclass · Answer

(B) The word $EXAMINATION$ consists of $11$ letters: $A, A, E, I, I, M, N, N, O, T, X$.To find the number of words before the first word starting with $E$,we must count all words starting with $A$.If we fix $A$ at the first position,we are left with $10$ letters: $A, E, I, I, M, N, N, O, T, X$.In these $10$ letters,$I$ occurs $2$ times and $N$ occurs $2$ times.The number of permutations of these $10$ letters is given by $\frac{10!}{2!2!}$.Calculation: $\frac{10 	imes 9 	imes 8 	imes 7 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1}{2 	imes 2} = 907200$.Therefore,there are $907200$ words starting with $A$,which appear before any word starting with $E$ in the dictionary.

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

Similar Questions

How many numbers can be formed from the digits $1, 2, 3, 4$ when the repetition is not allowed?

The number of $4$-digit even numbers that can be formed using $0, 1, 2, 3, 4, 5, 6$ without repetition is

The number of ways in which $10$ persons can go in two boats so that there may be $5$ on each boat,supposing that two particular persons will not go in the same boat is:

There are $15$ persons in a party and each person shakes hands with every other person exactly once. What is the total number of handshakes?

The number of arrangements of the letters of the word $PALANHAR$ in which no two vowels are together and exactly two vowels are at odd places,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module