The number of words of 5 letters that can be made with the letters of the word "PROPOSITION"
Text Solution
Verified by ExpertsA
Word is PROPOSITION
Here P’s = 2, O's = 3, Ι 's = 2 and T, R, N, S = 1
We have to made 5 letters words
Case Ι : When All 5 are different = 7p5 = 
= 2520
Case ΙΙ : When 2 alike ,3 different = 3C1 × 6C3 × 
= 3600
Case ΙΙΙ : When 2 alike , 2 alike, 1 different = 3C2 × 5C1 × 
= 450
Case IV : When 3 alike, 2 different = 1C1 × 6C2 × 
= 300
Case V : When 3 alike , 2 alike = 1C1 × 2C1 × 
= 20
So total required number = 6890
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