Dear Reader,

**IBPS PO** is starting in **5 months** (Oct, tentatively). You would know that “**Permutations and Combinations**” is a critical topic in PO exams. Once you understand concepts well, you can easily solve problems from Combinations. Below is a common type of problem witnessed by candidates in previous year PO exams.

**Example Problem:**

A box contains 4 apples, 7 oranges, and 8 bananas. If four fruits are picked at random, how many number of ways at least 2 apples will be selected?

**Solution:**

First, let us write down the **possibilities** for at least 2 apples in a draw of 4 fruits:

Possibilities for at least 2 apples =

(All 4 apples) OR

(3 apples AND (1 orange OR 1 banana )) OR

(2 apples AND 2 oranges) OR

(2 apples AND 2 bananas) OR

(2 apples AND 1 orange AND 1 banana) …equation 1

To solve this problem, we are going to apply a familiar formula:

Number of ways of selecting R items from N items is NCR

and **NCR = N!/(N-R)!R!**

Also, to solve equation 1 (and other similar equations in future) remember this: Replace **“AND”** with **“x”** (multiplication) and **“OR”** with **“+”**.

Let us now simplify equation 1 using the above logic and formula.

No of ways = 4C4 +

4C3 * (7C1 + 8C1) +

4C2 * 7C2 +

4C2 * 8C2 +

4C2 * 7C1 *8C1

Now if we calculate the combination values using the formula NCR = NCR = N!/(N-R)!R!, we will get:

No of ways = 1 + 4 * (7 + 8) + 6 * 21 +6 * 28 +6 * 7 * 8

= 1 + 60 + 126 + 168 + 336

= 691

Therefore, __your answer is 691__

We hope that the above problem and solution will help you. All the very best!

**IBPS Exams 2017** are beginning in **4-5 months** from now (PO in Oct and RRB in Sep, tentatively). Prepare fast and well to make use of the **big opportunity**. All the best.

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