Combination Solutions & Questions For IBPS, SBI

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:

ⁿC_r = n! / (r!)(n-r)!

Note:ⁿC_n = 1 and ⁿC₀ =1

ⁿC_r = 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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