The number of ways of arranging 8 boys and 8 | vedclass

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

Question

(D) There are two possible cases for sitting alternately:Case $1$: The arrangement starts with a boy: $B G B G B G B G B G B G B G B G$.The number of

Vedclass · Accepted Answer

$2!(8!)^2$

Vedclass · Answer

(D) There are two possible cases for sitting alternately:Case $1$: The arrangement starts with a boy: $B G B G B G B G B G B G B G B G$.The number of ways to arrange $8$ boys in $8$ positions is $8!$ and $8$ girls in $8$ positions is $8!$. So,$8! 	imes 8!$ ways.Case $2$: The arrangement starts with a girl: $G B G B G B G B G B G B G B G B$.The number of ways to arrange $8$ girls in $8$ positions is $8!$ and $8$ boys in $8$ positions is $8!$. So,$8! 	imes 8!$ ways.Total number of arrangements $= 8! 	imes 8! + 8! 	imes 8! = 2 	imes (8!)^2 = 2!(8!)^2$.

The number of ways of arranging $8$ boys and $8$ girls in a row so that boys and girls sit alternately is

Similar Questions

There are $m$ books in black cover and $n$ books in blue cover,and all books are different. The number of ways these $(m+n)$ books can be arranged on a shelf so that all the books in black cover are put side by side is

If all the letters of the word $CRICKET$ are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in the dictionary order,then the rank of the word $CRICKET$ is

How many words can be formed using the letters of the word $COURTESY$ such that the first letter is $C$ and the last letter is $Y$?

How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?

In how many ways can the letters of the word $PERMUTATIONS$ be arranged if the words start with $P$ and end with $S$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module