639 viewsDiscrete maths
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In a race with 30 runners where 8 trophies will be given to the top 8 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?

How many ways can you do the above problem if a certain person, Roberta, must be one of the top 3 winners?

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Anonymous 2 Comments

first part can be done in 30p8 ways.

if roberta is in top 3 then we have 29c7 ways to select seven winners.

among 7 we can distribute 7 trophies in 7c7*7! ways

and remaining 1 trophy in 1 ways. trophy should be either 1st 2nd or 3rd prize

since roberta can get only trophies of prize 1 ,2 ,3

this can be done in total 3*7c7*7!*29c7ways

in the second case too there are 8 prizes and 30 runners, isn’t it? but roberta has to get one of the top three prizes. see this problem as 8 positions and 30 objects where object roberta has to be fixed in only among first three positions

yes sir ur method is also correct ..according to u the no. of ways will be 3c1*29c7*7! ways.. actually sir in the abv ans i forgot to multiply 29c7 with 3*7c7*7!..now i have corrected it…thnks for telling another way to solve

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