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

2775 ways

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
`(n!)/(r!\cdot(n-r)!)`

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

`(75!)/(2!(75-2)!)`

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

After simplification we will get
`(75\cdot 74\cdot 73!)/(2!\cdot73!)`

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

after more simplification we will get
`(75\cdot 74\cdot)/(2!)`

Finally, we will get
`(75\cdot 74\cdot)/(2)=75\cdot37=2775`