Words of length 10 are formed using the lette | vedclass

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

Question

(A) The total number of letters available is $10$. For $x$,we form words of length $10$ with no repetition,which is a permutation of $10$ distinct let

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) The total number of letters available is $10$. For $x$,we form words of length $10$ with no repetition,which is a permutation of $10$ distinct letters: $x = 10!$. For $y$,we choose $1$ letter to be repeated twice from $10$ letters in $^{10}C_1$ ways. We then choose $8$ other letters from the remaining $9$ letters in $^9C_8$ ways. The total number of arrangements of these $10$ letters (where one is repeated twice) is $\frac{10!}{2!}$. Thus,$y = {}^{10}C_1 	imes {}^{9}C_8 	imes \frac{10!}{2!}$. Calculating the ratio: $\frac{y}{9x} = \frac{{}^{10}C_1 	imes {}^{9}C_8 	imes \frac{10!}{2!}}{9 	imes 10!} = \frac{10 	imes 9}{9 	imes 2} = 5$.

Words of length $10$ are formed using the letters $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated,and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then,$\frac{y}{9x} =$

Similar Questions

The value of $^n{P_r}$ is equal to

If $^nP_4 : ^nP_5 = 1 : 2$,then $n = \dots$

In how many ways can $8$ distinct toys be distributed among $5$ children?

The sum of all numbers formed by using all the digits $3, 1, 7, 9$ exactly once is:

The number of all possible three-letter words that can be formed by choosing three letters from the letters of the word $FEBRUARY$ so that a vowel always occupies the middle place is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module