A library has a copies of one book,b copies o | vedclass

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

Question

(A) The total number of books is $N = a + 2b + 3c + d$. We have $a$ identical copies of one book,$b$ identical copies of each of two books,$c$ identic

Vedclass · Accepted Answer

$\frac{(a + 2b + 3c + d)!}{a! (b!)^2 (c!)^3}$

Vedclass · Answer

(A) The total number of books is $N = a + 2b + 3c + d$. We have $a$ identical copies of one book,$b$ identical copies of each of two books,$c$ identical copies of each of three books,and $d$ distinct single books. The number of arrangements of $N$ items where there are $n_1$ identical items of type $1$,$n_2$ identical items of type $2$,etc.,is given by $\frac{N!}{n_1! n_2! \dots}$. Here,we have: - $a$ identical copies of one book ($a!$ ways) - $b$ identical copies of each of two books ($(b!)^2$ ways) - $c$ identical copies of each of three books ($(c!)^3$ ways) - $d$ single copies of $d$ books ($1!$ ways for each,so $1^d = 1$) Thus,the total number of arrangements is $\frac{(a + 2b + 3c + d)!}{a! (b!)^2 (c!)^3}$.

$A$ library has $a$ copies of one book,$b$ copies of each of two books,$c$ copies of each of three books,and single copies of $d$ books. The total number of ways in which these books can be arranged is:

Similar Questions

If the digits are not allowed to repeat in any number formed by using the digits $0, 2, 4, 6, 8$,then the number of all numbers greater than $10,000$ is equal to $....$

How many numbers between $3000$ and $4000$ can be formed using the digits $3, 4, 5, 6, 7, 8$ without repetition,such that the numbers are divisible by $5$?

$A$ coin is tossed $3$ times and the outcomes are recorded. How many possible outcomes are there?

How many words can be formed using the letters of the word $INSURANCE$,such that all vowels always come together?

Evaluate $8!$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module