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15 girls are seated at a round table. The
number of ways of selecting three girls such
that all the three are not seated together is
Options:
number of ways of selecting three girls such
that all the three are not seated together is
Solution:
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Verified Answer
The correct answer is:
440
The total number of ways selecting 3 girls from 15 girls seat around a round table is ${ }^{15} C_3$. Now, number of ways selecting 3 girls who sit together at one place is 15 .
$\begin{aligned}
\text { So, required number of ways } & ={ }^{15} C_3-15 \\
& =\frac{15 \times 14 \times 13}{3 \times 2}-15 \\
& =35 \times 13-15 \\
& =455-15=440
\end{aligned}$
$\begin{aligned}
\text { So, required number of ways } & ={ }^{15} C_3-15 \\
& =\frac{15 \times 14 \times 13}{3 \times 2}-15 \\
& =35 \times 13-15 \\
& =455-15=440
\end{aligned}$
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