Question

How many different ways are there to arrange the $6$ letters in the word $SUNDAY$ ?

• A. $280$
• B. $720$
• C. $1110$
• D. $56$

Answer 1

Answer: (B)

$720$

The first letter of the rearrangement can be any $1$ of $6$ letters.

The second letter can now be any $1$ of $5$ letters. So the first two letters can be combination of $6\times 5$ letters or $30$ arrangements.

The third letters can be any $1$ of $4$ remaining letters. So, the first three letters can be combination of $6\times 5\times 4$ letters or $120$ arrangements.

The fourth letter can now be only $1$ of $3$ remaining letters. So, the first four letters can be combination of $\times 5\times 4\times 3$ letters or $360$ arrangements.

The fifth letter can now be only $1$ of $2$ remaining letters, so, the first fours letters can be be a combination of $6\times 5\times 4\times 3\times 2$ or $720$ arrangements

The final letter can now be only one letters because all of the others have been used so, the six letters can be combination of $6\times 5\times 4\times 3\times 2\times 1$ letters or $720$. arrangements

Hence, the option $B$ is the correct answer.