Question

To play football, 7 students Omkar, Aditya, Ravi, Nishad, Rigved, Shantanu and Raghav went to the ground. After playing game for few minutes, they sit on the ground in a straight line.
Based on the above information, answer any four of the following questions:
i) Total number of ways of sitting arrangements of seven students is
(a) 5040 (b) 720 (c) 1440 (d) None of these
ii) Total number of arrangements of sitting if Nishad, Omkar and Rigved sit together is (a) 720 (b) 144 (c) 24 (d) 120
iii) Total number of arrangements if Aditya and Raunak are sitting at extreme position is (a) 24 (b) 240 (c) 120 (d) None of these
iv) Total number of arrangements if Shantanu is sitting in the middle is
(a) 720 (b) 36 (c) 72 (d) None of these
v) Total number of arrangements if Raghav , Rigved never sit together is (a) 1440 (b) 240 (c) 3500 (d) 3600

Answer 1

Answer:

the answer is 720 the answer is 720 the answer is 720

Answer 2

a) Total number of ways of sitting arrangements of seven students is 5040 ways.

a) Total number of arrangements of sitting if Nishad, Omkar and Rigved sit together is 720.

b) Total number of arrangements if Aditya and Raunak are sitting at extreme position is 240

d) Total number of arrangements if Shantanu is sitting in the middle is none of these.

d)  Total number of arrangements if Raghav , Rigved never sit together is 3600.

Step-by-step explanation:

Lets arrange first,

Omkar  Aditya  Ravi  Nishad  Rigved  Shantanu  Raghav.

Sit in straight line,

i) Total number of ways of sitting arrangements of seven students is 7!

7! = 5040.

Therefore, total number of ways of sitting arrangements of seven students is 5040 ways.

ii) If three people sit with each other always then it will be 3!5!

3!5! = 720

Therefore, total number of arrangements of sitting if Nishad, Omkar and Rigved sit together is 720.

iii) Total number of arrangements if Aditya and Raunak are sitting at extreme position is 2!5!

2!5! = 240.

Total number of arrangements if Aditya and Raunak are sitting at extreme position is 240

iv) Total number of arrangements if Shantanu is sitting in the middle is 2!3!6! =None of these.

v)  Total number of arrangements if Raghav , Rigved never sit together is = Total - Sit together = 7! - 6!2! = 3600

Therefore, total number of arrangements if Raghav , Rigved never sit together is 3600.