oout of 45 people ,37 caught the train,15 the bus,5 walked.how many caught both bus and train?
20
To find out how many people caught both the bus and the train, we need to use the principle of inclusion-exclusion.
First, let's find the total number of people who caught either the bus or the train. We have 37 people who caught the train, 15 people who caught the bus, and 5 people who walked.
Total number who caught either the bus or the train = number who caught the train + number who caught the bus - number who walked
= 37 + 15 - 5
= 47
Since this total is higher than the number of people (45) in the group, it implies that there is some overlap between those who caught the bus and those who caught the train.
Now, to find the number of people who caught both the bus and the train, we need to subtract the number of people who only caught either the bus or the train from the total number of people who caught either the bus or the train.
Number of people who caught both the bus and the train = Total number who caught either the bus or the train - number who only caught either the bus or the train
= 47 - 45
= 2
Therefore, 2 people caught both the bus and the train.