Question

India, Nepal, Pakistan, Bhutan and Sri Lanka have completed in volleyball tournament. The winners get in order of merit I, II or III prize. What is the probability of India securing any one of the prizes?

Answer 1

When India wins $I^{st}$ prize, the remaining $2$ prizes can be arranged in $4P_2$ ways.
Hence, number of permutations with India as a winner of $I^{st}Prize{=}^4{P}_2$
$\therefore$ Number of arrangements in which India can be the winner $=3{\times }^4{P}_2$
But $n\left(S\right){=}^5{P}_3$
$\therefore$ Probability of India securing any one of the prizes $=\frac{3{\times }^4{P}_2}{{}^5{P}_3}=\frac{3\times 4\times 3}{5\times 4\times 3}=\frac{3}{5}$