20. A bag contains 12 items of which 4 are defective. From this 2 item

1.	20. A bag contains 12 items of which 4 are defective. From this 2 items are drown atrandom. Find the probability of getting(i) no item defective(ii)one item defective Ga) both items defectiverds are drawn at random from a pack of 52 cards. Find the probability ofgetting all the four cards of the same number.
Answer» There are 4 suits in a standard deck 52 cards.Number of ways of selecting 4 cards out of 13 cards( i.e. a suit) are 13!/(4!9!)Note that we can choose 4 cards out of any 4 possible suits.So total ways become: P = 4 * ( 13!/9!4! ) Also, no of ways to select 4 cards out of 52 cards are: Q = 52!/(4!48!) Hence The probability is: P/Q = (4*13!/4!9!)/(52!/4!48!)

20. A bag contains 12 items of which 4 are defective. From this 2 items are drown atrandom. Find the probability of getting(i) no item defective(ii)one item defective Ga) both items defectiverds are drawn at random from a pack of 52 cards. Find the probability ofgetting all the four cards of the same number.

Answer»

There are 4 suits in a standard deck 52 cards.Number of ways of selecting 4 cards out of 13 cards( i.e. a suit) are

13!/(4!9!)Note that we can choose 4 cards out of any 4 possible suits.So total ways become:

P = 4 * ( 13!/9!4! )

Also, no of ways to select 4 cards out of 52 cards are:

Q = 52!/(4!48!)

Hence The probability is:

P/Q

= (4*13!/4!9!)/(52!/4!48!)