would appreciate your help checking if i did it cxorrectly
we have 7 girls and 13 boys standing in a line
1)x is a random variable defined by the number of the girls who stand in the last 5 places. what is p(x=i) for i=0,1,..5. my answer: $\frac{\binom{7}{i}\binom{13}{5-i}}{\binom{20}{5}}\:5!$
2)assuming that the places in the line are numbered. Y is the random variable defined by the smallest number of the location where a girl stands. what is p(y=j) when j=1,2,...,14? my answer: if we ave 7 girls, and we need the smallest number in where girls are located then it should be $\frac{\binom{13}{j-1}7}{\binom{20}{j}}$
3)if w is the random variable defined by the number of girls that to their right stands a boy, what is p(w=4)? i'm stuck on this one and i don't know how to solve it using the random variant w. would appreciate learning how to do it.
thank you very much for your help, did my best to elaborate and explain what i did