Question

BCU 102 ASSIGNMENT 3
1. Determine the number of combinations of the letters of the word EXAMINATION given th
four letters are taken at a time.
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Answer 1

answer

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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