Arrangements (1 Viewer)

[wagig]

This was in my half-yearly exam, not really sure how to approach it


i) There are 4 students, 3 teachers and 2 parents sitting around a table. How many arrangements can there be if the 4 students sit together, the 3 teachers sit together, and no student sits next to a teacher.
ii) A parent and a student are related. What is the probability that these two are sitting together.

 

[braintic]

This was in my half-yearly exam, not really sure how to approach it


i) There are 4 students, 3 teachers and 2 parents sitting around a table. How many arrangements can there be if the 4 students sit together, the 3 teachers sit together, and no student sits next to a teacher.
ii) A parent and a student are related. What is the probability that these two are sitting together.

(i)

Put the block of 4 students anywhere. You can arrange them in 4! ways.
The students at the ends of the block must sit next to a parent ... 2 possibilities.
The position of the block of teachers is then determines, all that is left to do is arrange them .... 3! ways.

4! times 2 times 3! = 288




(ii)

A parent must sit next to one, and only one, student. There is 1 chance in 4 that it is their relation.