1. An event organizer is planing a programme for a group of 20 people who want to embark on a sightseeing trip. Due to space constraints at the facilities to be visited the orga- nizer partitions the group into five non-empty subgroups. The number of people in the subgroups may vary from one subgroup to another. (a) How many different partitions are there for the organizer? (b) How many different partitions are there if the second subgroup is made up of 4 people? (c) How many different partitions are there if the fourth subgroup is made up of 6 people? (d) How many different partitions are there if the second and fourth subgroups have 4 and 6 people respectively? (e) The organizer chooses a partition of the people at random. Find the probability that the number of people in the second and fourth subgroups of the chosen partition are not 4 and 6 respectively.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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