How many ways a team of five salespersons can be formed from a group of 10...

How many ways a team of five salespersons can be formed from a group of 10 salesmen and 8 saleswomen, if the team contains at most 2 saleswomen?

Expert Solution

Total number off people is 10+8=18.

We are forming team of 5.

Now,

The number of teams of 5 can be formed with 0 saleswomen is

The number of teams of 5 can be formed with 1 saleswomen is

Since 1 saleswoman in team means other 4 are salesmen and 4 salesmen from 10 can be taken in ways

The number of teams of 5 can be formed with 2 saleswomen is

Since 2 saleswoman in team means other 3 are salesmen and 4 salesmen from 10 can be taken in ways and 2 saleswomen from 8 can be taken in ways

Hence the number of ways a team of 5 salespersons can be formed from the given group such that the team contains at most 2 saleswomen is

orchestra answered 2 years ago

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