Question

There are 20 movies available. If 10 of the choices are action, 6 of them are comedies and 4 of them are horror, what is the probability the first movie in t he marathon is an action film?

Answer 1

out of total 20 movies 10 are action, 6 are comedy and 4 are horror.

there are total 20_fact / ( 10_fact * 6_fact * 4_fact ) ways to select the movie in order of choosing non repetative and order does matter.

total ways to select all movies = 20_fact / ( 10_fact * 6_fact * 4_fact ) = 20*19*18*17*16*15*14*13*12*11 / ( 6*5*4*3*2*1*4*3*2*1 ) = 38798760

Number of ways first movie is action ( fixing 1st element )

out of total 19 movies 9 are action, 6 are comedy and 4 are horror.

there are total 19_fact / ( 9_fact * 6_fact * 4_fact ) ways to select the movie in order of choosing non repetative and order does matter.

total ways to select 1st movie being action = 19_fact / ( 9_fact * 6_fact * 4_fact ) = 19*18*17*16*15*14*13*12*11*10 / ( 6*5*4*3*2*1*4*3*2*1 ) = 19399380

P[ 1st movie being action ] = 19399380 / 38798760 = 0.5