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  4. The number of 3 letters words, with or without meaning which can be formed out of the letters of the word 'NUMBER' Statement I: When repetition of letters is not allowed is 120 Statement II: When repetition of letters is allowed is 216 . Choose the correct option.

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Q. The number of $3$ letters words, with or without meaning which can be formed out of the letters of the word 'NUMBER'
Statement I : When repetition of letters is not allowed is $120$
Statement II : When repetition of letters is allowed is $216$ .
Choose the correct option.

Permutations and Combinations

Solution:

I. Number of 3 letter words (repetition not allowed)
$=6 \times 5 \times 4=120$
(as first place can be filled in 6 different ways, second place can be filled in 5 different ways and third place can be filled in 4 different ways)
II. Number of 3 letter words (repetition is allowed)
$=6 \times 6 \times 6=216$
(as each of the place can be filled in 6 different ways)