The six letters of the word ORANGE are written on cards and laid out in a row in random order. What is the probability that the row both begins and ends with a consonant?

ORANGE has three consonants R, N, G and three vowels O, A, E, all six letters different. The first card is a consonant with probability 3/6; that consonant is then used up, so the last card is a consonant with probability 2/5 from the five cards left. Multiply: $(3/6)\times (2/5)=1/5$. Counting the long way agrees: $3\times 2\times 4$! = 144 favourable layouts out of 6! = 720. Trap $1/4=(3/6)\times (3/6)$ treats the two ends as independent and lets the same consonant serve twice. Trap 1/2 answers only 'begins with a consonant'. Trap 2/5 quotes the second factor alone.