Given:
There are 10 smartphones.
Out of 10, there are 7 good and 3 defective smartphones.
Explanation:
a) To find: The number of ways exactly 4 good smartphones are selected when buying 5 smartphones
The number of ways is,
[tex]\begin{gathered} ^7C_4\times^3C_1=\frac{7!}{(7-4)!4!}\times\frac{3!}{(3-1)!1!} \\ =\frac{7!}{3!4!}\times\frac{3!}{2!1!} \\ =\frac{5\times6\times7}{3\times2\times1}\times3 \\ =5\times7\times3 \\ =105\text{ ways} \end{gathered}[/tex]
b) To find: The number of ways atleast 3 good smartphones are selected when buying 5 smartphones
The number of ways is,
[tex]\begin{gathered} ^7C_3\times^3C_2+^7C_4\times^3C_1+^7C_5=\frac{7!}{(7-3)!3!}\times\frac{3!}{(3-2)!2!}+\frac{7!}{(7-4)!4!}\times\frac{3!}{(3-1)!1!}+\frac{7!}{(7-5)!5!}\frac{}{1!} \\ =\frac{7!}{4!3!}\times\frac{3!}{1!2!}+\frac{7!}{3!4!}\times\frac{3!}{2!1!}+\frac{7!}{2!5!} \\ =\frac{5\times6\times7}{3\times2\times1}\times3+\frac{5\times6\times7}{3\times2\times1}\times3+\frac{6\times7}{1\times2} \\ =5\times7\times3+5\times7\times3+3\times7 \\ =105+105+21 \\ =231\text{ ways} \end{gathered}[/tex]
Final answer:
a) 105 ways
b) 231 ways
