Task 9. Randomly arrange 10 volumes of the encyclopedia on the shelf. Calculate the probability that: a) the volumes will be arranged in ascending order, b) volumes 1 and 2 will be arranged next to each other, c) volume one will be set later than volume $ 2. $
Task 9. Randomly arrange 10 volumes of the encyclopedia on the shelf. Calculate the
a) the volumes will be arranged in ascending order,
b) volumes 1 and 2 will be arranged next to each other,
c) volume one will be set later than volume $ 2. $
Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or if the set is already ordered, a rearrangement of the elements of that set. It also refers to the process of changing the linear order of an ordered set.
For example, let us assume there are three persons A, B and C sitting beside each other. The different ways in which this sitting arrangement is possible are: ABC, ACB, BAC, BCA, CAB and CBA i.e. there will be 6 ways. Hence, the number of permutations of 3 different things is 6.
And the number of arrangements of n different things taken r at a time (where repetition is not allowed) is n(r).
Classical Definition of Probability: If there are n mutually exclusive, exhaustive and equally likely outcomes of a random experiment and n(A) of them are favorable to the occurrence of event A, then according to the Classical definition of Probability, the probability of A, denoted by P(A), is defined by the ratio of n(A) and n.
It is given by the formula,
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