(D) There are $10$ speakers in total. The total number of ways to arrange $10$ speakers is $10!$.In any arrangement,there are two possibilities for th

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(D) There are $10$ speakers in total. The total number of ways to arrange $10$ speakers is $10!$.In any arrangement,there are two possibilities for the relative order of $S_1$ and $S_2$: either $S_1$ speaks before $S_2$,or $S_2$ speaks before $S_1$.Since the condition is that $S_1$ must address only after $S_2$,we only consider the cases where $S_2$ appears before $S_1$.By symmetry,exactly half of the total arrangements satisfy this condition.Therefore,the required number of ways is $\frac{10!}{2}$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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$S_1, S_2, \ldots, S_{10}$ 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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TS EAMCET 2004 All TS EAMCET

A
$10!$
B
$9!$
C
$10 \times 8!$
D
$\frac{10!}{2}$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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$S_1, S_2, \ldots, S_{10}$ 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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