Question

In a group of equal number of men and women, 10% man and 45% women are unemployed.The probability that person selected at random'is
employed is $\frac{k}{8}$. Find the value of $k$.

Answer 1

Total number of ways of distributing 4 objects on 4 places$=4!=24$.
Number of ways in which all the four objects can occupy their places $=1$
If three objects occupy their places,$4^{th}$ will also do so.
This is included in the above case.If two objects occupy their places, remaining two can go wrong by occupying each other's position in only one way.
So number of ways in which only two objects can occupy their places ${=}^{4}C\times 1=6.$
If one object occupies its position, any one of the ramaining three can go wrong in 2 ways by occupying the positions of the other two.
So number of ways in which only one object can occupy its place ${=}^4{C}_1\times 2=8.$ $\therefore$
Total number of ways in which at least one object can occupy its place $=1+6+8=15$.
Hence total number $=24-15=9$
$\therefore$ Required prob.$=\frac{9}{24}=\frac{3}{8}.$