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Permutation and Combination Formula PDF for Bank Exams

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What is Permutation and Combination?

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What is Permutation in Bank Exams?

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What is Combination in Bank Exams?

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Permutation and Combination Formula for Bank Exams

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• Factorial of a natural number n.

n! = 1 × 2 × 3 × 4 × .......× n

• Permutation Formula for Bank Exams:

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

• Combination Formula for Bank Exams:

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

• The relationship between permutation and combination for r things taken from n things

nPr = r! × nCr

Difference Between the Permutation and Combination for Bank Exams

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Permutation and Combination Formula With Examples

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Example 1:  Determine the number of 5 card combinations out of a deck of 52 cards, if there is exactly one king in each combination.

Solution:

Given a deck of 52 cards

There are 4 king cards in a deck of 52 cards.

According to the given, we need to select 1 king card out of the 4 Ace cards

∴ The number of ways to select 1 king from 4 king cards is 4C1

⇒ More 4 cards are to be selected now from 48 cards (52 cards – 4 king cards)

∴ The number of ways to select 4 cards from 48 cards is 48C4

Number of 5 card combinations out of a deck of 52 cards if there is exactly one king in each combination = 4C1 × 48C4

= 4 × [48!/(44! 4!)]

= 4 × [(48 × 47 × 46 × 45 × 44!)/ (44! × 24)]

= 4 × 2 × 47 × 46 × 45

= 778320

Example 2: How many 4 digit numbers can be formed using the digits (1, 3, 4, 5, 7, 9) when repetition of digits is not allowed?

Solution:

The given digits are six.
The number of 4 digit numbers that can be formed using six digits is 

6P4 = 6 * 5 * 4 * 3 = 360

So there are 360 4 digit numbers that can be formed using the (1, 3, 4, 5, 7, 9).

Permutation and Combination Formula for Bank Exam: FAQs

Q. What is the formula for permutation?

A. Permutation nPr = (n!) / (n-r)!

Q. What is the formula for combination?

A. Combination nCr = (n!) / r!(n-r)!

Q. What is permutation and combination?

A. Permutation and combination are the ways to describe a group of objects by selecting them in a set and forming subsets.