GREERERPETON is an extinct amphibian that lived in the early

GREERERPETON is an extinct amphibian that lived in the early Carboniferous period, grew to approximately 5 feet in length, and lived in North America.
a) In how many different ways can the letters in GREERERPETON be arranged?
b) In how many different ways can the letters in GREERERPETON be arranged if the first letter
must be a N and the last letter must be an E?

Solution

there are 12 letters in this wrods. Hence 12!

Some letters repeat, these have to be divided. there are 3 R\'s, 4 E\'s.

Total number of arrangements=12!/3!*4!=2217600

b) There are 3 R\'s, 4 E\'s.

For the remaingn 5 places, we need to select form the remaning 5 letters.

When the letters are different

When the letters are the we need to select from 7 available choices this can be done in7*6=42 ways.

when the letters are same, there are 2 options.

total possibilites=42+2=44