Question

If a person tosses a coin 23 times, how many ways can he get 11 heads

Answer 1

Tossing a coin is a binomial experiment.

Now lets say there are 'n' repeated trials to get heads. Each of the trials can result in either a head or a tail.

All of these trials are independent since the result of one trial does not affect the result of the next trial.

Now, for 'n' repeated trials the total number of successes is given by

$_{r}^{n}\textrm{C}$

where 'r' denotes the number of successful results.

In our case $n=23$ and $r=11$,

Substituting the values we get,

$_{11}^{23}\textrm{C}=\frac{23!}{11!\times 12!}$

$\frac{23!}{11!\times 12!}=1352078$

Therefore, there are 1352078 ways to get heads if a person tosses a coin 23 times.