Five students A,B,C ,D and E are getting bored of their regular study. They go to the playground and sit in a straight line. Answer the following; i)Find the number of ways of sitting if A and D can sit together. ii)Find the total number of arrangements if B is sitting in the middle or if E is sitting in the extreme left.
Answers
Answer:
Solution
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Ram → R Shyam → S
No. of ways of arranging in which R & S together =4!×2!=48
No. of ways of arranging in which R & S not together = Total ways to arrange − No. of ways of arranging in which R & S together.
=5!−4!×2!
=120−48=72.
Answer:
There are 48 ways of sitting if B is sitting in the middle or if E is sitting in the extreme left.
Step-by-step explanation:
(i) We need to find the number of ways provided A and D sit together.
Let A and D be consider as a single unit say X
Now we need to arrange B , C , E , X
They can be arranged in 4! ways.
X itself can be arranged in 2! ways.
Therefore, the number of ways of sitting if A and D can sit together = 4! * 2!
= 48 ways.
Therefore, there are 48 ways of sitting if A and D can sit together.
(ii) Number of arrangements if B is sitting in the middle or E is on the extreme left.
= When B is in the middle + When E is on the extreme left.
No. of ways of sitting when B is in the middle ( _ _ B _ _ )
= 4 * 3 * 1 * 2 * 1 = 24 ways
No. of ways of sitting when E is on the extreme left ( E _ _ _ _ )
= 1 * 4 * 3 * 2 * 1 = 24 ways
Therefore, the total arrangements = 24 + 24 = 48 ways.
Therefore, there are 48 ways of sitting if B is sitting in the middle or if E is sitting in the extreme left.