The probability of picking 30 rare coins continuously from a set of 100 coins that has 41 rare coins in it. The question to be more clear is: **Total no. of coins: 100** **Rare coins in the set: 41** **What is the chance of picking up 30 rare coins continuously?** My attempts at solving it: First probability = $\frac{41}{100}$; Second probability = $\frac{40}{99}$; Third probability = $\frac{39}{98}$; ......; Thirtieth probability = $\frac{11}{70}$ Chances of getting 30 rare coins in a row = $\frac{41*40*39*........*11}{100*99*98*......*70} = \frac{41!}{11!} * \frac{70!}{100!}$ Am I on the right path to solving this question? Or is there an easier way? Thanks.

One other way to solve this.

$\frac{C(41,30)}{C(100,30)}$

$= \frac{\frac{41!}{30!*11!}}{\frac{100!}{30!*70!}}$

$= \frac{41!}{11!} * \frac{70!}{100!}$

And when calculations are too long you don't need to solve it. It becomes answer.