Question

An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?

Answer 1

See, the committee must include the male persons, it is our priority of all..

Answer 2

And the committee is of 3 persons, so in that, there can be at least one male employee..

Answer 3

Hey, are you there? I need a response at least..

Answer 4

yes sorry

Answer 5

so would it be a combination problem?

Answer 6

So, how can you form three member committee keeping atleast one male in it?

Answer 7

5C2?

Answer 8

The options can be:
One Male and two females OR
two males and one females OR
Three males and no female..

I have got three, do you agree or you have any other option?

Answer 9

but theres only 1 male....

Answer 10

I am MAD..

Answer 11

Kill me..

Answer 12

So, we have 1 male and two females as our ONLY option..

Answer 13

yea

Answer 14

So, 1 male to choose from 1 male only, and two females you can choose from 5 females.
So:
\[\implies ^5C_2 \times ^1C_1\]

Answer 15

The later term comes out to be \(1\) only..

Answer 16

so 10 right

Answer 17

So, yes, Good, you were right, it is 5C2, and YES, it is 10..

Answer 18

Good, thanks for teaching me.. :)

Answer 19

\(\dagger\)

Answer 20

awesome thanks