Question

If a coin is flipped 75 times, in how many ways could there be exactly two tails?

Answer 1

 I think the answer is 2774 but dont quote me on it

Answer 2

Answer:

2775 ways

Step-by-step explanation:

We have been given the case to choose exactly two tails when flipped 75 times  means  $^{75}C_2$

Since, $^nC_r$ is equal to $\frac{n!}{r!\cdot(n-r)!}$  

Here n =75, r=2 substituting the values we will get

$\frac{75!}{2!(75-2)!}$

$n!=n\cdot (n-1)\cdot (n-2).....1$

After simplification we will get  $\frac{75\cdot 74\cdot 73!}{2!\cdot73!}$

Cancel out the common term that is 73! we will get

after more simplification we will get $\frac{75\cdot 74\cdot}{2!}$

Finally, we will get $\frac{75\cdot 74\cdot}{2}=75\cdot37=2775$