(i)
![\[SERIES\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1852687fdf138b5820ffb8a1d0d71a72_l3.png "Rendered by QuickLaTeX.com")
There are
![\[6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dba464f544e5646eaa291e02993dca75_l3.png "Rendered by QuickLaTeX.com")
letters in the word
out of which
![\[2\text{ }are\text{ }Ss,\text{ }2\text{ }are\text{ }Es\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-49a38a46df671d8961ed4443579de961_l3.png "Rendered by QuickLaTeX.com")
and the rest all are distinct.
So by using the formula,
![\[n!/\text{ }\left( p!\text{ }\times \text{ }q!\text{ }\times \text{ }r! \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bc8ed54be481d1eefd9d7346604c447c_l3.png "Rendered by QuickLaTeX.com")
total number of arrangements
![\[=\text{ }6!\text{ }/\text{ }\left( 2!\text{ }2! \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-320e483b41a82904db1f7b7e79db12f9_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left[ 6\times 5\times 4\times 3\times 2\times 1 \right]\text{ }/\text{ }\left( 2!\text{ }2! \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9f0764e1f3e1db27cdf01a33818b84fc_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[=\text{ }6\times 5\times 3\times 2\times 1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0328f36589a74e15c50883fd5a191626_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }180\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-279cc98d00c29b402c7a23b870b29e14_l3.png "Rendered by QuickLaTeX.com")
(ii)
![\[EXERCISES\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5559722f4db2bf40ba29ecb508f067bf_l3.png "Rendered by QuickLaTeX.com")
There are
![\[9\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-eda27e23820084685a09a6f91d2210f2_l3.png "Rendered by QuickLaTeX.com")
letters in the word
out of which
![\[3\text{ }are\text{ }Es,\text{ }2\text{ }are\text{ }Ss\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-73fea4aa0537a794e46ee5213ee00cac_l3.png "Rendered by QuickLaTeX.com")
and the rest all are distinct.
So by using the formula,
total number of arrangements
![\[=\text{ }9!\text{ }/\text{ }\left( 3!\text{ }2! \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9f60ec5a6142de518df323b619ee1551_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left[ 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \right]\text{ }/\text{ }\left( 3!\text{ }2! \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-acde8fec7bdc39c6e98d76c60178e029_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[=\text{ }\left[ 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \right]\text{ }/\text{ }\left( 3\times 2\times 1\times 2\times 1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a37cc91a0ce564df6b5cd53cc17a196a_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }9\times 8\times 7\times 5\times 4\times 3\times 1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7cf64c024b50920dfca5eec1d90cf350_l3.png "Rendered by QuickLaTeX.com")
So,
![\[=\text{ }30240\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c6acf4891c71e0e53da047b018105509_l3.png "Rendered by QuickLaTeX.com")
