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15 persons are sitting around a circular table. The number of ways of selecting three persons at a time from them, such that the selected three did not sit together at one place is
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2130 Upvotes
Verified Answer
The correct answer is:
440
The total number of ways selecting 3 persons from 15 persons seat around a circular table is \({ }^{15} C_3\).
Now, number of ways selecting 3 persons who sit together at one place is 15 .
\(\begin{aligned}
\text {So, required number of ways } & ={ }^{15} C_3-15 \\
& =\frac{15 \times 14 \times 13}{3 \times 2}-15 \\
& =35 \times 13-15 \\
& =455-15=440
\end{aligned}\)
Hence, option (d) is correct.
Now, number of ways selecting 3 persons who sit together at one place is 15 .
\(\begin{aligned}
\text {So, required number of ways } & ={ }^{15} C_3-15 \\
& =\frac{15 \times 14 \times 13}{3 \times 2}-15 \\
& =35 \times 13-15 \\
& =455-15=440
\end{aligned}\)
Hence, option (d) is correct.
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