Answer to Question #194171 in Discrete Mathematics for Saoirse lei kjelbe

Question #194171

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
Expert's answer
2021-05-18T05:06:02-0400

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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