Five salesmen, A, B, C, D and E, of a company are considered for a three member trade delegation to represent the company at an international trade conference. What is the probability that A gets selected?

Correct option is A

Given:

3 member trade delegation to selected from five salesman A,B,C,D and e

Formula Used:

Probabilities and Combination

​$$Probability P(E) =\frac{Number \ of \ Favourable \ Outcomes }{Total\ Number \ of \ Outcomes}$$​​

​$$^nC_r = \frac{n!}{r!(n-r)!}$$​​

Solution:

First we need to determine the total number of ways to choose 3 members out of 5 using combination formula:

​$$^5C_3 = \frac{5!}{3!((5-3)!} = 10$$​​

Constructing the sample space{ABC, ABD, ABE, ACD, ACE, ADE, BCD, BDE, BCE, CDE}

To find probability of A we count the number of possibilities of A being selected in the delegation

{ABC, ABD, ABE, ACD, ACE, ADE}

Hence probability if A is selected  $$P(A) = \frac{6}{10} =\frac{3}{5}$$​​