In an IT company, there are a total of 110 employees including 50

Hi RudeyboyZ,

The question tells us about a company where the employees are either programmers or non-programmers. We are asked to find the minimum no. of employees that needs to be picked to ensure that we have either 3 male programmers or 3 female programmers.

I am putting up a diagram to help you understand the question better:



We are given in the question that there are 110 employees and 50 programmers. That would leave us with 60 non-programmers. Out of the 50 programmers we have 35 male programmers and the balance 15 as female programmers.

The question asks us the minimum no. of employees that must be selected to guaranty that we have 3 programmers of the same sex i.e. either 3 male programmers or 3 female programmers.

Since the question is asking to guaranty picking up of 3 programmers of same sex, that would mean we need to exhaust all the possibility of picking up the non-programmers and then start picking up the programmers.That can only be done if we pick all the non-programmers first and then start picking up the programmers.

So we can pick all the 60 non-programmers.

Since we are left with only programmers now, we can start picking them up. Picking up 3 programmers would not guaranty us 3 same sex programmers as there may be 2 male programmers and 1 female programmers. Similarly picking up 4 programmers may leave us with 2 male programmers and 2 female programmers.

Picking any one of the more programmers would give us 3 programmers of same sex. So we need to pick up a minimum of 60 + 4 + 1 = 65 employees to ensure that we have 3 programmers of the same sex.

Hope it's clear

Regards
Harsh