Question

If a coin is tossed 5 times, and then a standard six-sided die is rolled 4 times, and finally a group of two cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?

Answer 1

Answer

we know that coin has two possible outcomes, i.e. head and tails

So, tossing 5 times, gives us a total outcome =

We know that the dice has 6 possible outcomes, i.e. 1,2,3,4,5,6

So, rolling die 4 times gives us a total outcome = $64-6*6*6*6=1296$

We know that there are 52 cards in a deck

we have to select 2 cards at a time, i.e. combination problem with r =2 and n =52

So, number of ways =

Total number of possible outcomes = multilication of all three possible values from three cases

setting the values, we get

Total number of possible outcomes = 32*1296*1326 = 54,991,872 ways