Question

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.

• A. Only Statement I is correct
• B. Only Statement II is correct
• C. Both I and II are correct
• D. Both I and II are false

Answer 1

Answer: (C)

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)