Question

what is the gap method in combinations?

Answer 1

Answer:

Can somebody please explain the gap and the string method used in permutations and combinations (combinatorics) to solve certain types of problems such as finding the number of arrangements when a number of objects are not together or a number of objects are always together. My teacher was talking about these and I could not understand what he was saying. I searched the internet but could not find good resources.

Answer 2

The Gap method and combinations

Take the word SIGNATURE, and find permutations if

(a): no two vowels are together (used gap method)

(b): The letters S,G,N are together (used string method)

(a) There are 4 vowels which can be placed in the gaps between consonants in (64) ways, and the vowels and consonants can be permuted separately.

−S−G−N−T−R−(64)×4!×5!

(b) Clump SGN into a string SGN so there are 1+6=7 "objects"

The clumped string can be permuted in 3! ways, and the 7 objects in 7! ways, thus 7!∗3! ways

There can be many variations of such problems, and all letters may not be distinct as they are here, but the basic principles of the two methods will remain the same.

A gap analysis is a method of assessing the differences in performance between a business' information systems or software applications to determine whether business requirements are being met and, if not, what steps should be taken to ensure they are met successfully.

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