1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
Given that,
We have to find how many different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
We know that,
Total number of arrangements of 26 different letters= 26!
Let A be the number of arrangements that contains 'the' = 24! ( Total no. Of alphabet= 26 subtract the number That contains 'the' i.e, 3 and add one for 'the' 26-23+1=24)
Let B be the number of arrangements that contains 'aid' = 24! (Total no. Of alphabet minus number of letter in 'aid' and add 'aid' as an alphabet i.e, 26-23+1= 24)
Total no. Of arrangements that contains either sequence 'the' or 'aid'
A or B= (A)+(B)- (A intersection B)
24! +24! -22! = 1.239x10²⁴
Therefore, 1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
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