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Question
The number of the permutation of 4 letters that can be made out of the letters of the words EXAMINATION is
The number of the permutation of 4 letters that can be made out of the letters of the words EXAMINATION is
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Solution
The correct option is A 2454
In the word Examination,E-1,X-1,A-2,M-1,I-2,N-2,T-1,O-1 there are 8 distinct words.
Case I: All words are distinct
we can take 4 words from 8 distinct in 8C4 and we can arrange the 4 words in 4! ways.
Total number of ways=8C4*4! ways=1680
Case II:1 word is alike and 2 is distinct
There are 3 group of alike words .We can choose in 3C1 ways and the distinct words in 7C2 .We can arrange the words in 4! ways but two words are same so 4!/2! ways.
Total number of ways=7C2*3C1*4!/2!=756
Case III:Two are alike
Total number of ways: 3C2*4!/2!*2!=18
Total of ways in which 4 letter words can be made out of the word EXAMINATION:1680 +756 +18=2454
In the word Examination,E-1,X-1,A-2,M-1,I-2,N-2,T-1,O-1 there are 8 distinct words.
Case I: All words are distinct
we can take 4 words from 8 distinct in 8C4 and we can arrange the 4 words in 4! ways.
Total number of ways=8C4*4! ways=1680
Case II:1 word is alike and 2 is distinct
There are 3 group of alike words .We can choose in 3C1 ways and the distinct words in 7C2 .We can arrange the words in 4! ways but two words are same so 4!/2! ways.
Total number of ways=7C2*3C1*4!/2!=756
Case III:Two are alike
Total number of ways: 3C2*4!/2!*2!=18
Total of ways in which 4 letter words can be made out of the word EXAMINATION:1680 +756 +18=2454
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