Four-letter strings are formed using the letters of the word PRIME, no letter being used more than once within a string. How many such strings do NOT begin with P?

Strings of 4 letters taken from the 5 different letters, with no repeat: $5\times 4\times 3\times 2=120$. Those that DO begin with P have their first place fixed and fill the other three from the remaining 4 letters: $4\times 3\times 2=24$. So the answer is 120 − 24 = 96. Counting directly agrees: 4 choices for the opening letter, then $4\times 3\times 2$ for the rest, which is again 96 — note that P becomes available again once it is not the opening letter. Trap 120 counts every string and forgets the condition. Trap 24 reports the banned strings instead of the allowed ones. Trap 60 halves the total on the idea that 'P either opens the string or it does not, so it must be even'; in fact P opens only one string in five, that is 24 of the 120.