Question

A company hired 35 new employees and categorized them as per their joining dates. 21 had joined
before 28.02.2012 and 14 had joined after 28.02.2012. The new joinees were called for a meeting to
discuss any problem they faced at workplace. 3 representatives were chosen randomly to speak on
behalf of the rest. What is the probability of selecting of 2 employees who had joined before
28.02.2012 and 1 after 28.02.2012?
Options 84/187 126/2431

Answer 1

SOLUTION

GIVEN

• A company hired 35 new employees and categorized them as per their joining dates. 21 had joined before 28.02.2012 and 14 had joined after 28.02.2012.

• The new joinees were called for a meeting to discuss any problem they faced at workplace.

• 3 representatives were chosen randomly to speak on behalf of the rest.

TO DETERMINE

The probability of selecting of 2 employees who had joined before 28.02.2012 and 1 after 28.02.2012

EVALUATION

Total number of employees = 35

Now 3 representatives were chosen randomly

Number of ways

$\sf{ = {}^{35}C_3 }$

Number of employees joined before 28.02.2012 = 21

Number of ways of selecting of 2 employees who had joined before 28.02.2012

$\sf{ = {}^{21}C_2 }$

Number of employees joined after 28.02.2012 = 21

Number of ways of selecting of 1 employee who had joined after 28.02.2012

$\sf{ = {}^{14}C_1 }$

Hence the required probability

$\displaystyle \sf{ = \frac{ {}^{21}C_2 \times {}^{14}C_1}{ {}^{35}C_3} }$

$\displaystyle \sf{ = \frac{210 \times 14}{35 \times 17 \times 11} }$

$\displaystyle \sf{ = \frac{6 \times 14}{17 \times 11} }$

$\displaystyle \sf{ = \frac{84}{187 } }$

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