Question

Find the number of $5$ letter words, with or without meaning, which can be formed out of the letters of the word $AUGUST,$ where the repetition of the letters is not allowed.

• A. $3125$
• B. $120$
• C. $720$
• D. $50$

Answer 1

The correct option is B $120$

$AUGUST$

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 anyone of the $5$ letters $A,U,G,U,S,T$.

Following which, the second place can be filled in by anyone 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; following which, the fifth place can be filled in $1$ way.

Hence, the required number of words is
$5\times 4\times 3\times 2\times 1=120.$