If A = {letters of ALLAHABAD} and B = {letters of AHMEDABAD), then find
i)A UB
ii) A - B.
Also verify
that:
a) n(A - B) = n(A U B) – n(B)
b) n(A U B) = n(A) + n(B) - n(AN B)
Answers
Step-by-step explanation:
A Big Example
Suppose we wish to arrange n=5 people {a,b,c,d,e}
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Table 1 — Permutations of {a,b,c,d,e}
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Table 2 — Permutations of {a,b,c,d,e}, taken 3 at a time
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Table 3 — Combinations of {a,b,c,d,e}, taken 3 at a time
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For more explanation, let's visit the post Find Difference Between Permutations and Combinations With The Best Summary
Re: Combination problem
Post by HallsofIvy » Tue Mar 12, 2019 8:43 am
The first part is easy- if each name as n letters and each letter has only two possible values then there are \displaystyle 2^n2
n
possible names so \displaystyle 2^n2
n
islands. There is a ferry route between two islands if and only if their names differ by one letter. In the example with 3 letters, the island Aaa has a ferry route to Baa, Aba, and Aab. Since there are 3 letters in the name, there are 3 letters that can change. If each name has n letters then each island has ferry routes to n other islands. Since there are \displaystyle 2^n2
n
islands there would be \displaystyle n(2^n)n(2
n
) routes except[b] that each route involves [b]2 islands. To correct for that, divide by 2. There are \displaystyle n(2^{n-1})n(2
n−1