Question

(2) The letters in the word 'envelope are written on individual pieces of paper and placed in a hat. a If the 8 letters are selected randomly without replacing them, what is the probability an 'e' is selected second? b. If 8 letters are selected randomly with replacement, what is the probability an e' is selected second? c. If 4 letters are selected randomly without replacing them, what is the probability the letters come out in the order 'nope'? d. If 4 letters are selected randomly without replacing them, what is the probability the letters can be rearranged to spell nope"?

Answer 1

2
a)
probability of selecting other letter except 'e' first = 5/8
probability of selecting 'e' as 2nd letter without replacing any = 3/7
therefore, P('e' 2nd ) = (5/8)*(3/7) = 15/56

b)
probability of selecting other letter except 'e' first = 5/8
probability of selecting 'e' as 2nd letter without replacing any = 3/8
therefore, P('e' 2nd ) = (5/8)*(1/2) = 15/64

c)
P('n' 1st) = 1/8
P('o' 2nd) = 1/7
P('p' 3rd) = 1/6
P('e' 4th) = 3/5
therefore, P('nope') = (1/8)*(1/7)*(1/6)*(3/5) = 3/1680

d)
P('n' 1st) = 1/8
P('o' 2nd) = 1/7
P('p' 3rd) = 1/6
P('e' 4th) = 3/5
therefore, P('nope' as well as rearranged) = 4!*(1/8)*(1/7)*(1/6)*(3/5) = 72/1680 = 3/70