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Posted by: Priyanshi S. on 01.06.2021
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Case 1 : Exactly one digit repeated twice --
eg AABCD Words= 10C1 X 9C3 X {5!/2!} =50400
Case 2 : Exactly one digit repeated thrice --
eg AAABC Words= 10C1 X 9C2 X {5!/3!}= 7200
Case 3 : Exactly one digit repeated four times --
eg AAAAB Words= 10C1 X 9C1 X {5!/4!}= 450
Case 4 : Exactly one digit repeated five times --
eg AAAAA Words= 10C1 X {5!/5!}= 10
Case 5 : Exactly two digits repeated two times each --
eg AABBC Words= 10C2 X 8C1 X {5!/(2! 2!)}= 10800
Case 6 : Exactly two digits repeated one of them twice and the other thrice --
eg AAABB Words= 10C1 X 9C1 X {5!/(2! 3!)}= 900
FINAL ANSWER= Sum of all cases= 69760
Number of words with no digit repeated= 10x9x8x7x6= 30240
Total five letter words formed using 10 letters =10x10x10x10x10= 10^5
Number of words which have at least one letter repeated = Total words - Number of words with no digit repeated =
10^5 - 30240 = 69760
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