A lepidopterist wishes to estimate the frequency with which an unusual form of a certain species of butterfly occurs in a particular district. He catches individual specimens of the species until he has obtained exactly 5 butterflies of the form desired. Suppose that the total number of butterflies caught is equal to 25. Find the probability that 25 butterflies would have to be caught in order to obtain 5 of a desired form, if the relative frequency p of occurrence of butterflies of the desired form is given by (i) P = i, (ii) p = i.