How many different ways can the letters of word CONSTITUTION be arranged? How many of these will have the letter $N$ , both at the beginning and at the end?

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Solution

$C O N S T I T U I T I O N$
$O \times 2 I \times 2 T \times 3 N \times 2 C \times 1 S \times 1 U \times 1$
The total ways it can be
arrange $= \frac{12!}{2! 2! 3! 2!}$
If $N$ is first and last place
$= 2 \times \frac{10!}{2! 2! 3!} = \frac{10!}{2! 3!}$

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How many different ways can the letters of word CONSTITUTION be arranged? How many of these will have the letter N, both at the beginning and at the end?

CONSTITUITIONO×2I×2T×3N×2C×1S×1U×1The total ways it can bearrange=12!2!2!3!2!If N is first and last place=2×10!2!2!3!=10!2!3!

How many different ways can the letters of word CONSTITUTION be arranged? How many of these will have the letter $N$ , both at the beginning and at the end?

$C O N S T I T U I T I O N$
$O \times 2 I \times 2 T \times 3 N \times 2 C \times 1 S \times 1 U \times 1$
The total ways it can be
arrange $= \frac{12!}{2! 2! 3! 2!}$
If $N$ is first and last place
$= 2 \times \frac{10!}{2! 2! 3!} = \frac{10!}{2! 3!}$