A legislative committee consists of 4 Democrats and 6 Republicans. A delegation of 4 is to be selected to visit a small republic. a. How many different delegations are possible? b. How many delegations would have all Democrats? c. How many delegations would have 3 Democrats and 1 Republican? d. How many delegations would include at least 1 Republican? a. The 4 delegates can be selected 210 different ways. b. The 4 delegates can be selected 1 different ways if all 4 are Democrats. c. The 4 delegates can be selected 24 different ways if 3 are Democrats and 1 is a Republican. d. The 4 delegates can be selected 24 different ways if at least 1 is a Republican.
Added by Leslie B.
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This can be done using combinations: $$\binom{10}{4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$$ b. Show more…
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