Question

there are 12 republicans and 10 democrats...


how many different committees of six can be formed if no more than four are democrats?

@jim_thompson5910

Answer 1

having a committee with "no more than four are democrats" is the same as having a committee with at least two republicans

Answer 2

so that should simplify things a bit (and this helps explain why n C r = n C (n-r) is true )

Answer 3

so how will u write the equations?

Answer 4

you could do it this way



number of ways to have a committee with 0 democrats = (10 C 0)*(12 C 6)

number of ways to have a committee with 1 democrat = (10 C 1)*(12 C 5)

number of ways to have a committee with 2 democrats = (10 C 2)*(12 C 4)

number of ways to have a committee with 3 democrats = (10 C 3)*(12 C 3)

number of ways to have a committee with 4 democrats = (10 C 4)*(12 C 2)

Answer 5

then add up all those individual counts

Answer 6

ohhh thank you!!