Permutations & Combinations
1. The following four family groups, consisting of 6 adults and 12 children in total, are all going to the cinema together:
Mr and Mrs Mitchell and their two children
Mrs and Mrs Lee and their four children
Mr Kim and his three children
Ms Miller and her three children
Find the number of different ways that all 18 people can sit in a row of 18 seats if
(i) no adults are sat next to each other
(ii) each family group sits together.
Ai এর মাধ্যমে
১০ লক্ষ+ প্রশ্ন ডাটাবেজ
প্র্যাকটিস এর মাধ্যমে নিজেকে তৈরি করে ফেলো
উত্তর দিবে তোমার বই থেকে ও তোমার মত করে।
সারা দেশের শিক্ষার্থীদের মধ্যে নিজের অবস্থান যাচাই
The diagram below shows part of a train carriage. There are twenty-eight seats consisting of twenty normal seats, S, and eight table seats, T. In this part of the train carriage there is a group of twelve schoolchildren and two teachers, along with a married couple, four businessmen, and three backpackers.
Find the number of ways that the passengers could be arranged in this part of the train carriage if
(i) the passengers are arranged completely at random
(ii) all four businessmen want to sit together facing each other around one of the tables.
Given that everybody is arranged completely at random within this part of the train carriage, find the probability that
(i) the three backpackers are sat in the front and the two teachers are sat together on one side of the aisle
(ii) the schoolchildren are all on one side of the aisle and the married couple are sat together on the other side of the aisle.
If instead the 18 people are sat randomly in three rows of six, what is the probability that all of the adults will be sat in the back row?
