1 The numbers of \(\alpha\)-particles emitted per minute from two types of source, \(A\) and \(B\), have the distributions \(\operatorname { Po } ( 1.5 )\) and \(\operatorname { Po } ( 2 )\) respectively. The total number of \(\alpha\)-particles emitted over a period of 2 minutes from three sources of type \(A\) and two sources of type \(B\), all of which are independent, is denoted by \(X\). Calculate \(\mathrm { P } ( X = 27 )\).