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$S_1, S_2, \ldots \ldots, S_{10}$ are the speakers in a conference. If $S_1$ addresses only after $S_2$, then the number of ways the speakers address is
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The correct answer is:
$\frac{(10 !)}{2}$
Since, $S_1$ speak after $S_2$, therefore two places can be chosen out of 10 place is ${ }^{10} C_2$ ways and rest of the 8 speakers can speak in 8 ! ways.
$\therefore$ Required number of ways $={ }^{10} C_2 \cdot 8$ !
$$
\begin{aligned}
& =\frac{10 !}{2 ! 8 !} \cdot 8 ! \\
& =\frac{10 !}{2 !} .
\end{aligned}
$$
$\therefore$ Required number of ways $={ }^{10} C_2 \cdot 8$ !
$$
\begin{aligned}
& =\frac{10 !}{2 ! 8 !} \cdot 8 ! \\
& =\frac{10 !}{2 !} .
\end{aligned}
$$
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