COMBINATIONS (24 pts)
1. Patrick has assignments in 5 subjects. He can only do two assignments. In how many ways can he do two assignments? (3 pts)
2. In how many ways can a group of 5 men and 3 women be made out of a total of 10 men and 6 women? (3 pts)
3. A box contains 6 red, 5 blue and 3 white balls. In how many ways can we select 3 balls such that
a. They are of different colors? (3 pts)
b. They are all red? (3 pts)
c. Two are blue and one is white? (3 pts)
d. Exactly 2 are blue? (3 pts)
e. None is white? (3 pts)
f. At least two are white? (3 pts)
1.
"N=C^2_5=\\frac{5!}{3!2!}=10" ways
2.
"N=C^5_{10}\\cdot C^3_6=\\frac{10!}{5!5!}\\cdot \\frac{6!}{3!3!}=5040" ways
3.
a.
"N=C^1_6 \\cdot C^1_5\\cdot C^1_3=6\\cdot5\\cdot 3=90" ways
b.
"N=C^3_6=\\frac{6!}{3!3!}=20" ways
c.
"N=C^2_5\\cdot C^1_3=\\frac{5!}{2!3!}\\cdot \\frac{3!}{2!}=30" ways
d.
"N=C^2_5\\cdot C^1_9=\\frac{5!}{2!3!}\\cdot \\frac{9!}{8!}=90" ways
e.
"N=C^3_{11}=\\frac{11!}{8!3!}=165" ways
f.
"N=C^2_3\\cdot C^1_{11}+C^3_3=\\frac{3!}{2!}\\cdot \\frac{11!}{10!}+1=34" ways
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