In how many ways can the letters of the word CARPET be arranged

In so many ways ;

acre cape care carp cart cate pace pact pare part pate pear peat pert prat race atrapt rate reap race tape tare tarp tear tepatrapace act ape apt arc are art ate cap car cat cep ear eat era pack par pat pea pec per pet rap rat rec rep ret tap tar tea

And so on .

720

Explanation:

you would be using permutation i believe

because carpet has 6 letters you have six placement options

_x_x_x_x_x_

if you can only use the letters once

you can put all letters in p1

so 6x_x_x_x_x_

but because of that you would only be able to put all but one in p2 and one less than p2 in p3 going all the way to 1 in the last

so 6x5x4x3x2x1

i might be wrong but this has worked for me

What can we do about it

It is the top one. the answer is -7. that is smallest