Questions & Answers

Question

Answers

A. \[2 \times 16! \times 16!\]

B. \[4 \times 16! \times 16!\]

C. \[2 \times 8! \times 16!\]

D. None of these

Answer

Verified

129k+ views

* Permutation is an arrangement of all or a part of a set of objects keeping in mind the order of the selection. Number of ways n people can be seated in r seats is \[^n{P_r} = \dfrac{{n!}}{{(n - r)!}}\]

Two classes having 32 people in total can be arranged in 4 rows having 8 chairs each, and will be in the following 2 ways in Row1 Row2 Row3 Row4 respectively.

\[{1^{st}}\]way: Class1 Class2 Class1 Class2 or

\[{2^{nd}}\]way: Class2 Class1 Class2 Class1

Total arrangements = Total arrangements in \[{1^{st}}\] way+ Total arrangements in the\[{2^{nd}}\] way

We know from the formula \[^n{P_r} = \dfrac{{n!}}{{(n - r)!}}\], so if n=r then \[^n{P_n} = \dfrac{{n!}}{{(n - n)!}} = \dfrac{{n!}}{{0!}} = n!\]

Since we know each class has total number of students as 16, so

Number of arrangements made to seat 16 people of class1 in 16 chairs \[{ = ^{16}}{P_{16}} = 16!\]

Number of arrangements made to seat 16 people of class2 in 16 chairs \[{ = ^{16}}{P_{16}} = 16!\]

Arrangements in \[{1^{st}}\] way =\[16! \times 16!\]

Arrangements in\[{2^{nd}}\] way =\[16! \times 16!\]

Hence total arrangement = \[16! \times 16! + 16! \times 16!\] \[ = 2 \times 16! \times 16!\]