1
The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is .
Answer
1405
Solution
MATHS has 5 distinct letters. Each letter used must occur at least twice, so the multiplicities form a partition of 6 into parts 2.
(i) 6 : one letter six times 5 1 = 5
(ii) 4 + 2 : 5 4 6!4! 2! = 20 15 = 300
(iii) 3 + 3 : 5C2 6!3! 3! = 10 20 = 200
(iv) 2 + 2 + 2 : 5C3 6!2! 2! 2! = 10 90 = 900
total = 5 + 300 + 200 + 900 = 1405
Answer: 1405
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