Ten Different Letters of the Alphabet Are Given. Words with Five Letters Are Formed from These Given Letters. Then, the Number of Words that Have at Least One Letter Repeated Is. - Mathematics

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MCQ

Ten different letters of the alphabet are given. Words with five letters are formed from these given letters. Then, the number of words that have at least one letter repeated is.

Options

  • 69760

  • 30240

  • 99748

  • None of these

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Solution

69760
Explanation:
Total number of words = 105 = 100000 and the number of words in which no letter is 

repeated = `""^10P_5=(10!)/(5!)=30204`

Hence, the required number of words in which at least one letter is repeated = 100000 - 30240 = 69760

Concept: Permutation and Combination (Entrance Exam)
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