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riadik2000 [5.3K]
3 years ago
11

In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls ( 1 through 45) and matching the n

umber on the gold ballc( 1 through 34). If one ticket is purchased, what is the probability of winning the jackpot?
Mathematics
2 answers:
Serggg [28]3 years ago
4 0

Answer:

1 in  41,539,806.

Step-by-step explanation:

The number of ways to pick 5 numbers from 45 = 45C5

= (45*44*43*42*41) / (5*4*3*2*1)

= 1,221,759.

There are 34 ways to pick a gold ball so total number of ways to get  6 matching numbers is

1221759*34

= 41,539,806.

Lilit [14]3 years ago
4 0

Answer: \dfrac{1}{41539806}

Step-by-step explanation:

Given : Total white balls = 45

Number of correct balls needed to win = 5

Using combination ,

The total combination of getting 5 balls selected from 45 balls = ^{45}C_5=

Total gold balls = 34

Similar;y , Number of ways to select 1 ball out of 34 = ^{34}C_1

Total number of ways of selecting 5 white balls and 1 gold balls = ^{45}C_5\times^{34}C_1

Using combination formula ^nC_m=\dfrac{n!}{m!(n-m)!}

=\dfrac{45\times44\times43\times42\times41\times40!}{120\times40!}\times\dfrac{34!}{1!(34-1)!}\\\\=1221759\times34=41539806

i.e. Total number of possible ways of selecting 5 white balls and 1 gold balls =41539806

But there is only one combination for wining the jackpot.

So the probability of winning the jackpot= \dfrac{\text{Favorable}}{\text{Total}}=\dfrac{1}{41539806}

Hence, the required probability = \dfrac{1}{41539806}

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