Of a lot of 12 items 3 are defective a How many ways can we

Of a lot of 12 items, 3 are defective.

(a) How many ways can we choose different samples of 3 items.

(b) Find the number of samples of 3 items containing no defective

(d) Find the number of samples of 3 items containing 2 defective

(e) Find the number of samples of 3 items containing 3 defective

Total number of items = 12

number of defectives = 3

number of non defectives = 12 - 3 =9

(a) How many ways can we choose different samples of 3 items.

we have to select 3 items from 12 items this we can done by using combination

3 items can be selected from 12 items in (12 C 3) ways

12C3 = 12! / 3! * (12-3)!

12! = 12*11*10*9*8*7*6*5*4*3*2*1 = 479001600

3! = 3*2*1 = 6

9! = 9*8*7*6*5*4*3*2*1 = 362880

12 C 3 = 479001600 / (6 * 362880) = 220

b) Find the number of samples of 3 items containing no defective

Here we have to select 3 items containing no defective that is we have to select 3 non defectives from 9.

This can be done in 9C3 ways.

9C3 = 9! / 3! * 6!

9 C 3 = 84

c) Find the number of samples of 3 items containing 1 defective

Here we have to select 3 items containing 1 defective and 2 non defectives.

1 defective can be select from 3 this can be done in 3C1 =3 ways

and 2 non defectives can be selected from 9.

This can be done in 9C2 ways. = 36

number of samples of 3 items containing 1 defective = 36 * 3 = 108

d) Find the number of samples of 3 items containing 2 defective

Here we have to select 3 items containing 2 defectives and 1 non defective.

2 defectives can be selected from 3 in 3C2 ways = 3

1 non defective can be selected from 9 in 9C1 ways = 9

number of samples of 3 items containing 2 defective = 3 * 9 = 27

e) Find the number of samples of 3 items containing 3 defective

Here also we have to select 3 items containing 3 defectives and 0 are non defectives.

3 defectives can be done in 3 C 3 ways = 3

0 non defectives can be done in 9 C 0 ways = 1

number of samples of 3 items containing 3 defective = 3 * 1 = 3