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.
Answer: [tex]\dfrac{1}{41539806}[/tex]
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 = [tex]^{45}C_5=[/tex]
Total gold balls = 34
Similar;y , Number of ways to select 1 ball out of 34 = [tex]^{34}C_1[/tex]
Total number of ways of selecting 5 white balls and 1 gold balls = [tex]^{45}C_5\times^{34}C_1[/tex]
Using combination formula [tex]^nC_m=\dfrac{n!}{m!(n-m)!}[/tex]
[tex]=\dfrac{45\times44\times43\times42\times41\times40!}{120\times40!}\times\dfrac{34!}{1!(34-1)!}\\\\=1221759\times34=41539806[/tex]
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= [tex]\dfrac{\text{Favorable}}{\text{Total}}=\dfrac{1}{41539806}[/tex]
Hence, the required probability = [tex]\dfrac{1}{41539806}[/tex]
