Chapter 8.5, Problem 72E

(a)

To determine

To find: the number of ways can a vending company purchase four of these units and receive all good units.

Answer to Problem 72E

All units is good the purchase ways is 17550.

Explanation of Solution

Given Information:

A shipment of 30 flat screen televisions contains three defective units.

Calculation:

A shipment of 30 flat screen televidions contains three defective units. Company purchases four of these units.

Godd unit is $30-3=27$

All good unit mean,

  ${}_{27}{C}_4=\frac{27!}{\left(27-4\right)!4!}=17550$

Hence when all units is good the purchase ways is 17550.

(b)

To determine

To find: the number of ways can a vending company purchase four of these units and receive two good units and two bad mean,

Answer to Problem 72E

Two good units and two bad purchase ways is 1053.

Explanation of Solution

Given Information:

A shipment of 30 flat screen televisions contains three defective units.

Calculation:

A shipment of 30 flat screen televidions contains three defective units. Company purchases four of these units.

Godd unit is $30-3=27$

Two good units and two bad mean,

  $\begin{array}{c}{}_{27}{C}_2{\times }_3{C}_2=\frac{27!}{\left(27-2\right)!2!}\times \frac{3!}{\left(3-2\right)!2!}\\ =351\times 3\\ =1053\end{array}$

Hence when two good units and two bad purchase ways is 1053.

(c)

To determine

To find: the number of ways can a vending company purchase four of these units and receive at least two good units.

Answer to Problem 72E

At least two good unit purchase ways is 27378.

Explanation of Solution

Given Information:

A shipment of 30 flat screen televisions contains three defective units.

Calculation:

A shipment of 30 flat screen televidions contains three defective units. Company purchases four of these units.

Godd unit is $30-3=27$

At least two good unit mean,

  $\begin{array}{c}{}_{27}{C}_2{\times }_3{C}_2{+}_{27}{C}_3{\times }_3{C}_1{+}_{27}{C}_4{\times }_3{C}_3=\frac{27!}{\left(27-2\right)!2!}\times \frac{3!}{\left(3-2\right)!2!}+\frac{27!}{\left(27-3\right)!3!}\times \frac{3!}{\left(3-1\right)!1!}+\frac{27!}{\left(27-4\right)!4!}\times \frac{3!}{\left(3-3\right)!3!}\\ =351\times 3+2925\times 3+17550\times 1\\ =1053+8775+17550\\ =27378\end{array}$

Hence when at least two good unit purchase ways is 27378.