Question

-5- Question 5 (12 marks) Use a SEPARATE book clearly marked Question 5 Find the number of different ways 6 adults and 4 children can be seated in a row if: a (6) (c) there are no restrictions. lo! = 36288 there must be an adult on each end of the row. a P xPix = 1209603 two particular children must not be seated together. 2P2 IP q =7825765-3628800 -7257602893040 there must be at least two adults seated between any two children. 6 x 4P2 x 313x: (d) A farmer accidentally spreads a poisonous chemical on the soil in his field. The concentration of the chemical in the soil is initially 5 parts per million. One 1 dl 5 ota1111 1t+

Answer 1

1. a) There are 6 adults and 4 children = 10 people in total. Total number of ways in which we can arrange 10 objects = 10!

b) Two adults can be chosen in 6C2 ways and arranged at the end of the row in 2! ways. Rest of the 8 people can be arranged in 8! ways

Total ways = 6C2 * 2! * 8! = 6P2 * 8!

c) Number of ways in two particular children must not be seated together = Total number of possible ways - Number of ways in which two particular children are always together

If two particular children are always together, we will consider them a single object, hence there will be 9 objects in total. Number of ways in which two particular children are always together = 9!*2!

Total required ways = 10! - 9!*2!

d) If there must be atleast two adults seated between any two children, then the possibility is:

C A A C A A C A A C

Here, Children can only sit on the places of C and Adults on A

Total number of ways of arranging 4 children in 4 places = 4!
Total number of ways of arranging 6 adults in 6 places = 6!

Total required ways = 4!*6!