1. In how many orders may a coin show 3 tails & 2 heads after being tossed 5 times?
Required no. of ways= No. of ways in which the 3 heads (or the 2 tails) can be chosen out of the 5 tosses.
= 5C3( or 5C2) = 10.
2. Suppose we know there are 3 tails and 2 heads, what is the probability that the order is exactly HTHTT?
p= (.5)^5 = 1/32
probability of each outcome is .5; the combined probability is their product( as the events are independent)
3. Three cards are drawn from a deck of playing cards without replacement.
Find probability that there are 1 picture card and 2 aces in that order?