Answer to Question #191395 in Statistics and Probability for Zethembiso

Question

In a lottery. Players must match five numbers plus a bonus number. White balls are chosen from 59 white balls numbers 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

Question:-

In a lottery players must match 5 numbers plus a bonus Number white balls are chosen from 59 white balls number from 1 to 59 and 1 red ball( The bonus number ) is chosen from 35 red balls number 1 to 35. how many different results are possible?

solution:-

According to question player must match 5 number plus a bonus number

in other word players must match total six numbers (5 numbers chosen from 1 to 59 from 59 white balls number 1 to 59, similarly Bonus number { 6th number } chosen from 35 red balls numbered 1 to 35 .now, we start chosen white and red balls and get different ways as below.

5 white balls out of 59 balls can be selected in different way

=⁵⁹C₅

= 59!/5!54!

=59×58×57×56×55×54!/5!54!

=59×58×57×56×55/5!

=59×58×57×56×55/120 (where 5!=120)s

One red ball out of 35 balls can be selected in different ways

=35

now 6 number selected in different way

=[59×58×57×56×55/120]×35

{here We want combination of 5 ball and one red ball so we multiply both }

now solve above, and we get

=175223510 possible results.