Find the number of words formed by permuting all the letters

Question

of the word INDEPENDENCE such that the E's do not come together.

Answer 1

Use the "backdoor" approach,
that is
find the number of ways when they are together.

then we have EEEE, I, N,N,N,D,D,P,C
arrange 9 things, with 3N's and 2 D's
= 9!/(3!2!)
= 30240

number of arrangements without restriction
= 12!/(4!3!2!) = 1663200

so number of ways when they are not together
= 1663200 - 30240 = 1632960

Answer 2

great answers