Find  the  number of  5  card combinations out  of  a  deck  of   52  cards, if  there is  exactly  one ace in each  combination

Number of ways  selecting  one ace from 4 aces  ${ }^4{C}_1$ 
Number of ways  selecting  4  cards out  of 48  cards  = ${ }^{48}{C}_4$
Hence  , by FPC , 5  cards out  of  52 cards  with  exactly  one  ace  can be  selected in  ${ }^4{C}_1{\times }^{48}{C}_4$ ways 
$=4\times \frac{48\times 47\times 46\times 45}{24}$

${[}^n{C}_1=nand{}^n{C}_4=\frac{n(n-1)(n-2)(n-3)}{24}]$

$=\frac{48\times 47\times 46\times 45}{6}$

$8\times 47\times 46\times 45$

$=778320 ways$