# Combination Solutions & Questions For IBPS, SBI – PO/CLERK

## Combination Solutions & Questions For IBPS, SBI – PO/CLERK

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In the following article, the topic ’Combinations’ from Quantitative aptitude is discussed.

## COMBINATIONS SOLUTIONS

Combinations : Each of the different combinations possible which can be formed by taking some or all of a number of objects is called a combination.

Example: – Suppose we want to select two out of three boys X, Y, Z then,

Possible combinations are XY, YZ & ZX.

Please note that XY and YX represent the same combination here.

A number of Combinations possible of n different things taken r at a time is given by:

nCr = n! / (r!)(n-r)!

Note:nCn = 1 and nC0 =1

nCr = nC(n-r)

Example: Find the value of       (i) 100C98        (ii) 50C 50

Sol:(i) 100C98 = 100C(100-98)

= 100 * 99 / 2 *1

= 4950

(ii) 50C50 = 1

Example: In how many ways can a cricket team of eleven players be selected out from a batch of 15 players?

Sol: Required number of ways:

= 15C 11 = 15C (15-11) = 15C 4

= 15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1

= 1365

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Example: In how many ways can a committee of 5 members be selected from among 6 men & 5 ladies consisting of 3 men and 2 ladies?

Sol: (3 men out of 6) and (2 ladies out of 5) are to be selected

So, required number of ways

=(6C3 * 5C2)

= 200

Example: Out of 7 constants and 4 vowels, how many words with or without meaning consisting of 3 consonants and 2 vowels can be formed from them?

Sol: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)

= 7C3 * 4C2

= 210

Number of combinations each having 3 consonants and 2 vowels = 210

As each combination contains 5 letters

Number of ways of arranging 5 letters among themselves

= 5! = (5 * 4 * 3 * 2 * 1)

= 210

So, required number of words = (210 * 210)

= 44100

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August 25, 2019