6. Suppose we have n cats and m dogs. In how many ways can you a.arrange them al

Question

6. Suppose we have n cats and m dogs. In how many ways can you

a.arrange them all in a line?

b.arrange them in a line where species alternate and n=m?

c.arrange them in a line where species alternate and n>m?

d.arrange them in a line where species alternate and n<m?

7. How many ways can a committee of six people be assembled to serve on a grant review panel from a group of 15 engineers, 12 computer scientists, and 10 mathematicians

a. if the committee needs at least 3 mathematicians?

b. if the committee cannot have more than 4 engineers?

c.if the committee needs a chair and a co-chair?

8. How many bitstrings of length 20

a.heve exactly 8 ones?

b.have either 8 ones or 9 zeros?

c.have exactly 6 ones and every 1 must be followed by at least two zeros?

Explanation / Answer

6. Assuming that animals of the same species are identical to each other, i.e. there cant be any relative arrangement between them.

a) (n+m)! / (n! * m!) = (n+m)Cm = (n+m)Cn

b) 2

c) (n-m)^m

d) (m-n)^n

7. a) 10C3 * (15+12+7)C3 = 718080

b) 22C6 + 15C1*22C5 + 15C2*22C4 +15C3*22C3 15C4*22C2 = 2253713

c) 37*36*35C4 = 69743520

8. Assuming that the first digit is always non-zero i.e. 1.

a) 19C7 = 50388

b) 19C7 + 19C9 = 142766

c) 36

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.