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  • In how many distinct ways can 25 students be arranged around a circular table, if 6 students are absent on that day and 10 students went to sports meet?Option: 1

In how many distinct ways can 25 students be arranged around a circular table, if 6 students are absent on that day and 10 students went to sports meet?

Option: 1

40,320


Option: 2

68,526


Option: 3

98,632


Option: 4

39,916


Answers (1)

best_answer

Ans: The correct answer is option d, 40,320

To calculate the number of distinct ways 25 students can be arranged around a circular table when 6 students are absent and 10 students went to a sports meet, we need to consider the remaining 25 - 6 - 10 = 9 students who are present.

The number of distinct ways to arrange the 9 present students around a circular table is \mathrm{(n-1) !}
In this case, n = 9, so the number of distinct ways to arrange the 9 present students around a circular table is \mathrm{(9-1) !=8 !}

Calculating \mathrm{8 !}, we get:
\mathrm{8 !=8 \times 7 \times 6 \times \ldots \times 3 \times 2 \times 1=40,320}

Therefore, there are 40,320 distinct ways to arrange the 25 students around a circular table when 6 students are absent and 10 students went to a sports meet.

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Gaurav

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