There are 10 distinct letters of the English | vedclass

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

Question

(A) The total number of $5$-letter words that can be formed using $10$ distinct letters (with repetition allowed) is $10^5 = 100000$.The number of $5$

Vedclass · Accepted Answer

$69760$

Vedclass · Answer

(A) The total number of $5$-letter words that can be formed using $10$ distinct letters (with repetition allowed) is $10^5 = 100000$.The number of $5$-letter words that can be formed using $10$ distinct letters without any repetition is given by the permutation formula $^{10}P_5 = \frac{10!}{(10-5)!} = 10 	imes 9 	imes 8 	imes 7 	imes 6 = 30240$.The number of words with at least one letter repeated is the total number of words minus the number of words with no repeated letters.Required number of words = $100000 - 30240 = 69760$.

There are $10$ distinct letters of the English alphabet. Words of $5$ letters are formed using these letters. How many such words can be formed if at least one letter is repeated?

Similar Questions

How many $5$-digit numbers can be formed using the digits $1$ and $2$,such that exactly one digit is different from the others?

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.

How many distinct words can be formed using the letters of the word $ARRANGE$ such that the two $A$'s do not occur together?

Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do all the vowels always occur together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module