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  • In how many distinct ways can 36 students be arranged around a circular table, if 5 students are absent on that day and 6 students went to sports meet?Option: 1<

In how many distinct ways can 36 students be arranged around a circular table, if 5 students are absent on that day and 6 students went to sports meet?

Option: 1

66,022,789


Option: 2

40,320,526


Option: 3

65,789,125


Option: 4

39,916,800


Answers (1)

To calculate the number of distinct ways 25 students can be arranged around a circular table when 5 students are absent and 8 students went to a sports meet, we need to consider the remaining 25 - 5 - 8 = 12 students who are present.

The number of distinct ways to arrange the 12 present students around a circular table is \mathrm{(n-1) !}.
In this case, n = 12, so the number of distinct ways to arrange the 12 present students around a circular table is \mathrm{(12-1) !=11 !}.
Calculating  \mathrm{11 !}, we get:

\mathrm{11 !=11 \times 10 \times 9 \times \ldots \times 3 \times 2 \times 1=39,916,800}
Therefore, there are 39,916,800 distinct ways to arrange the 25 students around a circular table when 5 students are absent and 8 students went to a sports meet.

Posted by

Kshitij

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