Question

Find the number of arrangements of the letters of the word $INDEPENDENCE.$ In how many of these arrangements

• A. $1663200$
• B. $25485$
• C. $2478945$
• D. $145896$

Answer 1

The correct option is A $1663200$

In word INDEPENDENCE

There are $3$N , $4$E , $2$D , $1$I , $1$P and $1$C

Since letter are repeating so we use this formula $\frac{n!}{P_1!P_2!P_3!}$

Total letter $=12$

So, $n=12$

Since, $3N,4E,\&2D$

$P_1=3,P_2=4,P_3=2$

total arrangement $=\frac{12!}{3!4!2!}$

=$1663200$.