DISCRETE MATH The board of directors of a pharmaceutical corporation has 10 memb

Question

DISCRETE MATH

The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholders' meeting is scheduled to approve a new slate of company officers (chosen from the 10 board members).

a) How many different slates consisting of a president, vice president, secretary, and treasurer can the board present to the stockholders for their approval?

b) Three members of the board of directors are physicians. How many slates from part (a) have

(i) a physician nominated for the presidency?
(ii) exactly one physician appearing on the slate?
(iii) at least one physician appearing on the slate?

Explanation / Answer

It is given that the board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholders' meeting is scheduled to approve a new slate of company officers (chosen from the 10 board members)

(A)

we are given to choose different slates consisting of a president, vice president, secretary, and treasurer can the board present to the stockholders for their approval

It means that there are four positions and each position is unique or distinct

4 slates from 10 member can be obtained as 10*9*8*7

=5040........Answer

(B)

Three members of the board of directors are physicians

(i)

we have to find number of slates when a physician nominated for the presidency

we know that the 5040 of each guy will be nominated for presidency in exactly 5040/10 times

now, we are given that there are three physicians

so, the number of times a physician would be nominated for presidency as (5040/10)*3=1512........Answer

(ii)

we are given that there is exactly one physician appearing on the slate

assume that the 7 non physicians and one physician

Total slates with or without a physician would be 8*7*6*5 = 1680

now, we find total slates without physician

so, we get

total slates without physician = 7*6*5*4=840

now, we find number of slate for exactly one physicians = 1680-840=840

now, we know that there can be first , second and third physicians

so, it will be repeated thrice

Hence , total times when exactly one physician appearing on the slate = 840*3=2520........Answer

(iii)

now, we have to find for at least one physician appearing on the slate

we have got total number of possible slates=5040

slates with no physicians = 7*6*5*4=840

now, the remaining slates have at least one physician is 5040-840 = 4200.........Answer

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

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