It is an important topic in Qualitative aptitude. Generally, 1-2 questions can be asked from this in the exams. Here three things Permutations, Combinations and Probability as their application are discussed below one by one.
Permutations - In this, the arrangement of a certain number of things in a particular order is done. Here order matters while arranging the things.
Combinations - In this, things will be selected from the collection of that thing. Here order does not matter.
Probability - It is the possibility of occurring any event. It can be from 0 to 1.
Permutation
$$n{_{P}}{_{_{r}}} = \frac{n!}{(n-r)!}$$
Combination
$$n{_{C}}{_{_{r}}} = \frac{n!}{(n-r)! \times r!}$$
Here n = total number of things
r = selection or arrangement of the number of things.
Probability
Probability of occurring an event = $$\frac{\text{Favourable outcome}}{\text{Total outcome}}$$
Total probability = Probability of occurring an event + Probability of not occurring an event.
Probability of occurring an event + Probability of not occurring an event = 1
Q) How many different ways can the letters of the word MANAGER be arranged?
Sol. Number of ways can the letters of the word MANAGER be arranged = $$\frac{7!}{2!}$$
= 2520
Q) In a bag, there are four red, five green and three yellow balls. Find out the probability of picking three balls from the bag such as at least two of them are red.
Sol.
Probability of picking three balls from the bag such as at least two of them are red = $$\frac{4_{C_{2}} \times 8_{C_{1}}+ 4_{C_{3}} }{12_{C_{3}}}$$
= $$\frac{48+4}{220}$$
= $$\frac{52}{220}$$
= $$\frac{13}{55}$$
