B Now suppose that you had N coins create an mathematical ex

B. Now suppose that you had N coins, create an mathematical expression that would allow you to culate how many different ways you could create a string of flips that would give heads and 0N-M) tails Neoins that have choose the first many different ways You could choose a of coins? could since we don\'t care what the then one of the remaining N-i in of permuting heads and get the heads or tails in, you to divided by the number of ways the N without respect tails. This result is call the number of ways of choosing M objects out of a set of of to order. (What you are to for this part of the problem is justify the expression for the number combinations in terms of the relevant factorials by describing the choosing and arranging process)

Solution

Suppose N coins are tossed prob of getting head =0.5 and tail =0.5

As there are only two outcomes, and each event is independent we take X the no of heads in tossing N coins as a variables

X follows binomial distribution with parameters p for each success and N no of trials.

Suppose m heads to be obtained in tossing N coins probability

= NCm (0.5)3(0.5)N-3 provided all coins are fair

Thus X can take values as

0 1 2 3 4 5 6 .... m .... N

No of ways 1 N NC2 NC3 NCm   ... NCN=1

Where C represents combination.

Explanation is suppose you want to get m heads these m heads can appear in any order in N coins i.e. NCm ways are there to get m heads.