Timothy is re-arranging his marble collection. he has five identical blue marbles, five identical green marbles and three identical black marbles he can fit exactly five marbles into a case and must have at least one of each. how many different ways can he arrange the case in?

720

Step-by-step explanation:

Knowing that he must place one of each type, the total number of marbles must be one of theses 6 cases:

3 blues, 1 green, 1 black

2 blues, 2 green, 1 black

2 blues, 1 green, 2 black

1 blues, 2 green, 2 black

1 blues, 1 green, 3 black

1 blues, 3 green, 1 black

At the same time, each case can be ordered in many ways, for example in the first option:

blue, blue, blue, green, black

blue, blue, blue, black, green

blue, blue, black, blue, green

et cetera

The total number of permutations for each case is 5! = 120

Taking into account the 6 cases, 6 x 120 = 720

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation:

are you an artist's daughter? cuz dang you a fine piece of art, girl.