Question

A 6-letter “word” is formed by selecting 6 of the 26 letters without replacement. Let A1...

A 6-letter “word” is formed by selecting 6 of the 26 letters without replacement. Let A1 be the set of all words beginning with X and A2 be the set of all words ending with Y. Find the number of distinct words in (a) ?,∩?., (b) ?,∪?..

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Answer #1

A) A1 \cap A2

A1 :

26 letters

X __ __ __ __ __

25*24*23*22*21 ways

=6375600

A2 :

__ __ __ __ __ Y

25*24*23*22*21 ways

=6375600

A1 \cap A2

X __ __ __ __ Y

=> 24*23*22*21 Ways

=> 255024

B)

A1 U A2 => A1 + A2 - A1 \cap A2

=> 6375600 + 6375600 - 255024

=> 12496176

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