Probability- Gravner -17.a

Question

A bag contains $80$ balls numbered {1, . . . , 80}. Before the game starts, you choose $10$ different numbers from among {1, . . . , 80} and write them on a piece of paper. Then $20$ balls are selected (without replacement) out of the bag at random.

(a) What is the probability that all your numbers are selected?

Answer 1

Total no. of possible  outcomes are $\binom{80}{20}$

Since all the 10 numbers are matched with the 20 picked balls,

the probability that all the numbers are selected= $\frac{\binom{10}{10} \times \binom{70}{10}}{\binom{80}{20}}$

Comments

pls explain 3^rd step