Find the number of 5 letter words, with or without meaning, which can be formed out of the letters of the word MARIO , where the repetition of the letters is not allowed ___ .
Find the number of 5 letter words, with or without meaning, which can be formed out of the letters of the word MARIO , where the repetition of the letters is not allowed
There are as many words as there are ways of filling in 5 vacant places by the 5 letters, keeping in mind that the repetition is not allowed.
The first place can be filled in 5 different ways by any of the 5 letters M,A,R,I,O.
Following which, the second place can be filled in by any of the remaining 4 letters in 4 different ways, following which the third place can be filled in 3 different ways; following which, the fourth place can be filled in 2 ways. At last, the fifth place can be filled in 1way by the letter remaining after filling the first 4 places.
Thus, the number of ways in which the 5 places can be filled, by the multiplication principle, is 5×4×3×2×1=120.
Hence, the required number of words is 120.
There are as many words as there are ways of filling in 5 vacant places by the 5 letters, keeping in mind that the repetition is not allowed.
The first place can be filled in 5 different ways by any of the 5 letters M,A,R,I,O.
Following which, the second place can be filled in by any of the remaining 4 letters in 4 different ways, following which the third place can be filled in 3 different ways; following which, the fourth place can be filled in 2 ways. At last, the fifth place can be filled in 1way by the letter remaining after filling the first 4 places.
Thus, the number of ways in which the 5 places can be filled, by the multiplication principle, is 5×4×3×2×1=120.
Hence, the required number of words is 120.
