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Consider a lottery game that is played by drawing five white balls out of a drum of 69 white balls (numbered 1–69) and one red ball out of a drum of 24 red balls (numbered 1–24). The jackpot is won by matching all five white balls in any order and the red ball.

(a) Find the possible number of winning numbers.
winning number(s)

(b) Find the possible number of winning numbers if the jackpot is won by matching all five white balls in order and the red ball.
winning number(s)

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MrRoyal

The order of selecting the balls is an illustration of permutation and combination

  • The possible number of winning numbers is 269724312
  • The possible number of winning numbers in order is 32366917440

The possible number of winning numbers

The given parameters are:

  • Total white balls = 69
  • Total red balls = 24

The possible number of winning numbers in any order is calculated using the following combination expression

[tex]n = ^{69}C_5 * ^{24}C_1[/tex]

This gives

[tex]n = 11238513* 24[/tex]

Evaluate the product

[tex]n = 269724312[/tex]

Hence, the possible number of winning numbers is 269724312

The possible number of winning numbers in order

When order is important, we make use of permutation.

So, we have:

[tex]n = ^{69}P_5 * ^{24}P_1[/tex]

This gives

[tex]n = 1348621560* 24[/tex]

Evaluate the product

[tex]n = 32366917440[/tex]

Hence, the possible number of winning numbers in order is 32366917440

Read more about permutation and combination at:

https://brainly.com/question/1216161