(a)[2]
Determine how many different arrangements can be made from the $10$ letters in SHOPKEEPER if all $3$ Es are kept together.
(b)[4]
Determine how many different arrangements of the $10$ letters in SHOPKEEPER are possible if the Ps are separated.
(c)[2]
Determine the probability that a randomly selected arrangement of the 10 letters in SHOPKEEPER begins with an E and also ends with an E.
(d)[3]
From the 10 letters of SHOPKEEPER, choose four letters. Find how many different selections there are if the four letters contain exactly one P.