# Crack IBPS PO 2017: Score Easy In A Common Type Of Combination Problem

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