Six students A B C D E F are to give speeches to the class T

Six students A, B, C, D, E, F are to give speeches to the class. The order of speaking is determined by random selection. Find these probabilities.

P(E will speak first)

P(C will speak fifth and B will speak last)

P(A or B will speak first)

there are 6! = 720 permutations of the letters ABCDEF

a) P(E will speak first)

E will speak: E _ _ _ _ _

remaining 5 postions can be filled in 5!

P = 5!/6! = 1/6

b) P(C will speak fifth and B will speak last)

_ _ _ _ C B

first 4 positions can be filled in 4! = 24 ways

P = 24 / 720 = 1 / 30

c) P(A or B will speak first)

we can have following options ...

A _ _ _ _ _ _ = 5! or 120 ways

or

B _ _ _ _ _ _ = 5! or 120 ways

P = (120+120) / 720 = 1/3