This is seventh chapter of IBPS Quantitative Aptitude Online course. I will cover Probability and Permutation and Combination in this chapter. These two are complex confusing topics. I will be giving key formulas which will make your task easier.

In case you have not read the chapter six please do so.Below is link to chapter six

**Permutation and Combination **

Permutation

The number of ways a number of objects can be arranged by taking all of them or specified number of them is called Permutation. The ordering matters in Permutation.

Combination

The number of ways a specified number of objects can be taken out of given number of objects is called Combination. The ordering does not matter in Permutation.

Formulas

Formula 2

The number of ways n items can be arranged in a circle is !(n-1) (that is factorial of n-1) . But if you have to arrange in a necklace then number of ways will be [!(n-1)] / 2

Formula 3

If N items are arranged in a row the number of ways in which they can be deranged so that none of them occupies original place is given by

!n (1/!0 – 1/!1 + 1/!2 +…+ (-1) to the power of n /!n)

Formula 4

Number of ways we can arrange N items out of which P are of one kind Q are of kind and R are of one kind is

N! / (P!Q!R!) that is factorial of N divided by factorial of P , Q and R.

Formula 5

Number of ways you can divide N similar items in R distinct groups where groups can be empty are are

(n+r-1)! / (r-1)! n!

that is factorial n+r-1 divided by factorial r-1 and factorial n

Formula 5

Number of ways you can divide N similar items in R distinct groups where no group is empty are

(n-1)! / (r-1)! (n-r)!

that is factorial n -1 divided by factorial r-1 and factorial n-r

Formula 6

The number of ways N distinct things can be arranged in R distinct groups where the order of items in group does not matter is

r to the power n

Formula 7

The number of ways N distinct things can be arranged in R distinct groups where the order of items in group does matter is

(n+r-1)! / (r-1)!

that is factorial of n+r-1 divided by factorial of r-1.

**Probability**

For example number of possible events in a dice (ludo game) is 6. The chance of getting 1 is 1. SO probability of getting 1 if a dice is thrown is 1/6.

The value of Probability will always be greater than equal to 0 or less than equal to 1

0<= P <= 1.

Formula 1

Probability of an event which is certain to happen is 1. For example probability of winning race if you alone are running is 1 as it is certain event only you can win it

Formula 2

Probability of an event which is certain to happen is 0. For example probability of winning race if you are not running in it is 0 as it is impossible event as you are not running in it.

Formula 3

Two events are mutually exclusive if they both can not occur together. For example if you throw a dice then only one number will occur you can not have two numbers at the same time.

Let A and are two mutually exclusive events then probability of happening A or B is

P(A+B) = P(A) + P(B)

where P(A) is probability of happening A and P(B) is probability of happening B.

If they are not mutually exclusive then

P(A+B) = P(A) + P(B) – P(A-B) where P(A-B) is probability of happening both A and B.

Formula 3

Two events are mutually independent if they both can occur together. For example if you throw two dice then number in one is independent of number of the second.

Let A and B are two independent events then probability that both will occur is given by

P(A) * P(B)

where P(A) is probability of happening A and P(B) is probability of happening B.

Formula 4

The probability of occurrence of event B when it is known that event A already occurred is given by

P(B/A) = P(A & B) / P(A)

where P(A&B) is probability of occurrence of event A and B and P(A) is probability of occurrence of event A.

With this we come to end of Chapter 7. We will cover remaining topics in next chapters. Feel free to post your queries and share this post. It will help others.