Question

In order to conduct an experiment 5 subjects are randomly selected from a group of 40 subjects how many different groups of 5 subjects are possible

Answer 1

Answer:

This can be done using the choose function.

The number of combinations are given by:

(

n

k

)

=

n

!

k

!

(

n

−

k

)

!

where

n

is the total number of students and

k

is the number of students to be picked. So we have

n

=

20

and

k

=

5

:

(

20

5

)

=

20

!

5

!

(

20

−

5

)

!

=

20

!

5

!

15

!

Evaluate directly with a calculator:

20

!

5

!

15

!

=

15504

we can simplify this before calculation by hand:

20

!

5

!

15

!

=

20

×

19

×

...

×

2

×

1

5

×

4

×

3

×

2

×

1

×

(

15

×

...

×

1

)

=

(

20

×

...

×

16

)

(

15

×

...

×

1

)

(

5

×

...

×

1

)

(

15

×

...

×

1

)

=

(

20

×

...

×

16

)

15

×

...

×

1

(

5

×

...

×

1

)

15

×

...

×

1

=

(

20

×

19

×

18

×

17

×

16

)

(

5

×

4

×

3

×

2

×

1

)

Simplify the numbers matched up by color:

=

(

4

×

19

×

9

×

17

×

4

)

(

1

×

1

×

3

×

1

×

1

)

=

(

4

×

19

×

3

×

17

×

4

)

(

1

×

1

×

1

×

1

×

1

)

=

3

×

4

×

4

×

17

×

19

=

48

×

323

=

15504