(10 points) Consider the following technique of shuffling a deck of n cards: For any initial ordering of the cards, go t

[answerhappygod]

(10 points) Consider the following technique of shuffling a deck
of n cards: For any initial ordering of the cards, go through the
deck one card at a time and at each card , flip a coin with
probability p of getting a head . If the coin comes up heads, then
leave the card where it is; if the coin come up tails, then move
the card to the end of the deck. After the coin has been flipped n
times, say that one round has been completed. For instance, if n=4
and the initial ordering is 1,2,3,4, then if the successive flips
result in the outcome H,T,T,H, then ordering at the end of the
round is 1,4,2,3,
a) What is the probability that the ordering after one round is
the same as the initial ordering?
b) If the coin is a fair coin (p=0.5), what will be the
numerical value of the probability in (a)?