Question

Two friends compete with each other and five other, equally good, violinists for first and second chair in an orchestra, in a blind competition What is the probability that the two friends end up as first and second chair together?

Answer 1

Answer: 0.0476

Step-by-step explanation:

Given : Two friends and 5 other people compete with each other for first and second chair in an orchestra.

Total people in this competition= 2+5=7

By permutation , Number of ways to arrange 7 people= 7!

Also, number of ways for two friends end up as first and second chair together= 2 × 5!   [ 2 ways to arrange friends on first and second chair and 5! ways to arrange others]

I.e. Required probability = $\dfrac{2\times5!}{7!}$

$=\dfrac{2!\times5!}{7\times6\times5!}\\\\=\dfrac{1}{7\times3}\\\\=\dfrac{1}{21}\\\\=0.0476$

Hence, the probability that the two friends end up as first and second chair together = 0.0476