harder Five cards are drawn from a new bag with 100 cards wh

[harder] Five cards are drawn from a new bag with 100 cards where 60 are blue and 40 are red. What is the probability of having 3 reds and 2 blues without regards to any order of the cards? [harder] Five cards are drawn from a new bag with 1000 cards where 600 are blue and 400 are red. What is the probability of having 3 reds and 2 blues without regards to any order of the cards?

Solution

e)

No. of ways of selecting 3 red cards = 40C3

No. of ways of selecting 2 blue cards = 60C2

Probability ( 3 Red and 2 Blue) = (40C3 * 60C2) / 100C5

= 0.232 Answer

f)

No. of ways of selecting 3 red cards = 400C3

No. of ways of selecting 2 blue cards = 600C2

Probability ( 3 Red and 2 Blue) = (400C3 * 600C2) / 1000C5

=((400!/(3!*397!)) *( 600!/(2!*598!))) / (1000!/(5!*995!))

=((398*399*400)/6)) *(599*600)/2)) / (1000!/(5!*995!))

=0.231 Answer

= 0.232 Answer