Question

Find the number of permutations of the first 10 letters of the alphabet, taking 3 letters at a time.

1040



980



720



630

Answer 1

720

Explanation:

The permutation looks like this for that set of data:

`_(10)P_(3)`

and the formula to solve it like this:

`_(10)P_(3) =(10!)/((10-3)!)`

which simplifies down to

`_(10)P_(3) =(10!)/(7!)`

Since every number less than 8 in the numerator cancels out with the denominator, we have

`_(10)P_(3)=10*9*8`

which equals 720