Question

How do you find the number of permutations of the first 13 letter of the alphabet taking 4 letters at a time?

Answer 1

`""_13C_4 = 13*11*5 = 715`

Explanation:

This Combinatorials, given by
`""_nC_k =(""_nP_k)/(k!) =((n), (k)) = color(red)((n!)/(k!(n-k)!))`
In your case `n=13, k=4` thus
`""_13C_4 = ((13!)/(4!*9!)) = 13*12*11*10*cancel(9!)/(cancel(9!)*4!)`
`""_13C_4 = (13*cancel12*11*cancel10^5)/(cancel(4*3)*cancel2)`
`""_13C_4 = 13*11*5 = 715`