Question

India, Nepal, Pakistan, Bhutan and Sri Lanka have competed in a 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

 Hint:The probability that India secures 1st rank is the same as securing 2nd and 3rd prizes. Calculate the total number of ways India can be in top three to get the probability.

Complete step-by-step answer:
Let India win the I prize. Therefore, there are four remaining teams as Nepal, Pakistan, Bhutan and Sri Lanka. In addition, there left II and II prizes. So these 2 prizes can be arranged between the rest four countries in \[^{4}{{P}_{2}}\] ways.
Hence, the number of permutations with India as a winner of the I prize is \[^{4}{{P}_{2}}\].
Again, it is equivalent to India securing II or II prize. So, the total number of permutations in which India can be in the top three is \[3{{\times }^{4}}{{P}_{2}}\].
Now there are a total 5 teams India, Nepal, Pakistan, Bhutan and Sri Lanka and 3 spots as I, II and III. So, Total number of possible permutations = \[^{5}{{P}_{3}}\].
Therefore, the probability of India securing any one of the prizes = \[\dfrac{3{{\times }^{4}}{{P}_{2}}}{^{5}{{P}_{3}}}\] = \[\dfrac{3}{5}\].
Hence, the probability of India securing any of the prizes is \[\dfrac{3}{5}\].

Note: There are 3 spots and 5 teams to compete. So, it can be said from here directly that there is \[\dfrac{3}{5}\] probability of India getting any of these ranks.