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