UPSC NDA Math Model Paper 4

The event of drawing first three red marbles from the bag can be written as:
P(1 red marble) AND P(1 red marble) AND P(1 red marble)
= P(1‌st red marble) × P(2‌nd red marble) × P(3‌rd red marble)
Since the marbles are drawn without replacement:
P(1st red marble ) =

‌7C1

‌21C1

=

7

21

=

1

3

P(2nd red marble ) =

‌6C1

‌20C1

=

6

20

=

3

10

P(3rd red marble) =

‌5C1

‌19C1

=

5

19

∴ Required probability =

1

3

×

3

10

×

5

19

=

1

38

.