Question

In a lottery, players must match five numbers plus a bonus number. Five white balls are chosen from 59 white balls numbered from 1 to 59, and one red ball (the bonus number) is chosen from 35 red balls numbered 1 to 35,how many different results are possible?

Answer 1

5 white balls out of 59 can be selected in $C_{59}^5$ ways. 1 red ball out of 35 can be chosen in 35 ways. Then the number of ways to compose a ticket is $C_{59}^5 \cdot 35 = \frac{{59!}}{{5! \cdot 54!}} \cdot 35 = \frac{{55 \cdot 56 \cdot 57 \cdot 58 \cdot 59 \cdot 35}}{{120}} = {\rm{175223510}}$

Answer: 175223510 results