What is the short hand (the "line 0 line" part at the very end) at the very end denoting? I assume they are implying the value equates to 0? Any insight on this would be appreciated :)

Solution. Given that - Let us Consider a cookie jars each have 25 cookies and whenever cookie Monster gets hungry . He Selects a cookie uniformly at random from either one . - Let "(" denote the number of cookies left in a jay when the other jas becomes empty . - Finding the probability that there are K Cookies, left P (c = K ) 25 100.300 258 ( A ) ( B )-7 P ( C = K ) is probability that there are k Cookies in one jax ( Say B ) and o in other. . cookies ase choosen at fandomly -> Rcookies in jax B left => 25 Cookies from A and (25 -K ) cookies from B taken . This is Same as assaging 50-k ( 25 + ( 25- K ) cookies ofder with 25 from A similarly odded with 25- k from B. . . N ( C =K ) = N Cassanging Foo- k in order ) ( choosing k from 25) N ( 50 - K ) ! 25 f , X C 25 ! ( 25 - K ) ! K ( 50 - K ) ! X 25! ( 25 - K ) ! ( 25 - K ) ! K !\f