Let

L $=$ In$1,$ n$2,.,$n$20\}$ be a list $20$ distinct in$-$

tegers. The integers in the list are randomized and then inserted in an array A$[1...20]$ of size

$20.$ See outline of an algorithm below. It starts with an initial count of 'zero'. If an element A$[$i$]<$ A$(20],$ then line $4$ increments the count by one and Ali$]$ is moved to A$[20]$

FINDTHENUMBEROFTIMESA$[20]$IsUPDATED$($A$)$

$1$ COUNT $=0$

$2$ FOR i $=1$ TO $19$

$3$

IF Ali$]<$ A$|20]$

$4$

COUNT $=$ COUNT $+1$

$5$

A$[20]=$ A$[$i$]$

$6$ return COUNT

$($a$)[10$ points$]$ What is the expected number of times line $4$ of the algorithm will be ex$-$ecuted, that is$,$ how many times the expression $($A$[$i$]<$ A$[20])$ is expected to be true.