10 different letters of English alphabet are given. Out of these letters, words of 5 letters are for

English

Gujarati

Hindi

6.Permutation and Combination

medium

$10$ different letters of English alphabet are given. Out of these letters, words of $5$ letters are formed. How many words are formed when at least one letter is repeated

A

$99748$

B

$98748$

C

$96747$

D

$97147$

Solution

(a) Number of words of $ 5$ letters in which letters have been repeated any times =${10^5}$

But number of words on taking 5 different letters out of $10 = {\,^{10}}{C_5} = 252$

Required number of words = ${10^5} – 252 = 99748$.

Standard 11

Mathematics

Share

Similar Questions

In how many ways can a student choose a programme of $5$ courses if $9$ courses are available and $2$ specific courses are compulsory for every student?

medium

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these

four cards are of the same suit,

medium

How many numbers greater than $1000000$ can be formed by using the digits $1,2,0,2,4,2,4 ?$

medium

Ten persons, amongst whom are $A, B$ and $C$ to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is

medium

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is

normal