(adsbygoogle = window.adsbygoogle || []).push({}); 1)The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholder's meeting is scheduled to approve a new slate of company officers (chosen from the 10 board members).

A)4 (Presendent, Vice Presendent, secretary, and treasurer) positions needs filled. How many possible ways are there to do it?

10 x 9 x 8 x 7

B)Three members of the board of directors are physicians. How many slates from part (A) have a physician nominated for presendency?

3 x 9 x 8 x 7 ????

C)How many slates have exactly one physician?

3 x 7 x 6 x 5

D)How many slates have at least one physician?

3 x 9 x 8 x 7

2)There are 3 cities: a, b, c. City a has two roads that go to C and 4 roads that go to b. City b has 3 roads that go to c.

A)How many ways can you get from a to c?

2 + (4x3)

B)How many round trips from a to c are there such that the return trip is at least partially different than the route taken to get there?

(2 + (4x3)) x (2 + (4x3)) - (2 + (4x3)) ????

3)If n is a positive integer and n is greater than 1, prove that c(n, 2) + c(n-1/2) is a perfect square.

I have no idea

4)A gym coach must select 11 seniors to play on a football team. If he can make his selection in 12,376 ways, how many seniors are eligible to play?

n! / (11! x (n-11)!) = 12,376

n! / (n-11)! = 12,376(11!)

That's all I got

5)How many ways can 10 identical dimes be distributed among five children if:

A)There are no restrictions?

c(14,10)

B)Each child gets at least one dime?

c(9,5)

C)The oldest child gets at least two dimes?

c(12,8)

I know those are the answers, but I don't know why.

6)Determine the number of integer solutions of:

x1 + x2 + x3 + x4 = 32

where:

A)xi >= 0, 1<= i <=4

c(35, 32)

B)xi > 0, 1<= i <=4

c(31, 28) Why?

C)x1, x2 >= 5, x3, x4 >= 7

c(11, 8) Why?

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# Homework Help: Discrete Math HW Check

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